Method for iteratively creating a matrix from base elements

A method for iteratively generating a matrix of base elements, the method comprising:

• first forming at least one base matrix containing at least all base elements, wherein said at least one base matrix may also contain empty elements, said empty elements being positions that are not occupied by one of the base elements;
• applying modification operators iteratively, which are able to transform the base matrix or any matrix arising therefrom into a modified matrix;
• applying expansion operators iteratively, which form a larger matrix from a plurality of optionally modified smaller matrices from the preceding iteration by copying, rotation or reflection by virtue of parts of the larger matrix being filled with the optionally modified smaller matrices;
• performing virtual experiments within the scope of which the properties of a created matrix are examined by systematic creation of values deliberately containing errors from which an error signal is derivable;
• and
• in order to create a complex matrix, forming all permutations of next larger matrices by applying expansion operators and then evaluating by means of virtual experiments, the next larger matrices selected with the smallest error signals, and then forming the next larger matrices successively therefrom by applying expansion operators and evaluating by means of virtual experiments until the error signal drops below a given limit.

An arrangement of a plurality of four different base elements (1,2,3,4) into a 16×16 matrix, wherein:

• a) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,4,3,2,1,3,4,1,2,4,3,2,1,3,4], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the fourth row of the 16×16 matrix have the arrangement [2,1,3,4,1,2,4,3,2,1,3,4,1,2,4,3], those in the fifth row of the 16×16 matrix have the arrangement [3,4,2,1,4,3,1,2,3,4,2,1,4,3,1,2], those in the sixth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the seventh row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the eighth row of the 16×16 matrix have the arrangement [4,3,1,2,3,4,2,1,4,3,1,2,3,4,2,1], those in the ninth row of the 16×16 matrix have the arrangement [1,2,4,3,2,1,3,4,1,2,4,3,2,1,3,4], those in the tenth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the eleventh row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the twelfth row of the 16×16 matrix have the arrangement [2,1,3,4,1,2,4,3,2,1,3,4,1,2,4,3], those in the thirteenth row of the 16×16 matrix have the arrangement [3,4,2,1,4,3,1,2,3,4,2,1,4,3,1,2], those in the fourteenth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the fifteenth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the sixteenth row of the 16×16 matrix have the arrangement [4,3,1,2,3,4,2,1,4,3,1,2,3,4,2,1], or
• b) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,3,4,2,3,4,1,1,4,3,2,4,3,2,1], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,1,4,3,2,2,3,4,1,1,2,3,4], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,4,1,2,3,3,2,1,4,2,1,4,3], those in the fourth row of the 16×16 matrix have the arrangement [2,1,4,3,3,2,1,4,4,1,2,3,3,4,1,2], those in the fifth row of the 16×16 matrix have the arrangement [4,1,2,3,3,4,1,2,2,1,4,3,3,2,1,4], those in the sixth row of the 16×16 matrix have the arrangement [3,2,1,4,2,1,4,3,3,4,1,2,4,1,2,3], those in the seventh row of the 16×16 matrix have the arrangement [2,3,4,1,1,2,3,4,4,3,2,1,1,4,3,2], those in the eighth row of the 16×16 matrix have the arrangement [1,4,3,2,4,3,2,1,1,2,3,4,2,3,4,1], those in the ninth row of the 16×16 matrix have the arrangement [1,4,3,2,4,3,2,1,1,2,3,4,2,3,4,1], those in the tenth row of the 16×16 matrix have the arrangement [2,3,4,1,1,2,3,4,4,3,2,1,1,4,3,2], those in the eleventh row of the 16×16 matrix have the arrangement [3,2,1,4,2,1,4,3 3,4,1,2,4,1,2,3], those in the twelfth row of the 16×16 matrix have the arrangement [4,1,2,3,3,4,1,2,2,1,4,3,3,2,1,4], those in the thirteenth row of the 16×16 matrix have the arrangement [2,1,4,3,3,2,1,4,4,1,2,3,3,4,1,2], those in the fourteenth row of the 16×16 matrix have the arrangement [3,4,1,2,4,1,2,3,3,2,1,4,2,1,4,3], those in the fifteenth row of the 16×16 matrix have the arrangement [4,3,2,1,1,4,3,2,2,3,4,1,1,2,3,4], those in the sixteenth row of the 16×16 matrix have the arrangement [1,2,3,4,2,3,4,1,1,4,3,2,4,3,2,1], or
• c) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2, 3,4,1,2,3,4,1,2], those in the fourth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], those in the fifth row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4], those in the sixth row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the seventh row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2], those in the eighth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], those in the ninth row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4], those in the tenth row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the eleventh row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2], those in the twelfth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], those in the thirteenth row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4], those in the fourteenth row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the fifteenth row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2], those in the sixteenth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], or
• d) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the fourth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the fifth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the sixth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the seventh row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the eighth row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the ninth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the tenth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the eleventh row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the twelfth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the thirteenth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the fourteenth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the fifteenth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the sixteenth row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1].

An arrangement of a plurality of four different base elements (1,2,3,4) into a 32×32 matrix, wherein:

• a) the base elements in the first row have the arrangement [12341234 23412341 12341234 23412341], those in the second row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the third row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the fourth row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the fifth row of the 32×32 matrix have the arrangement [12341234 23412341 12341234 23412341], those in the sixth row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the seventh row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the eighth row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the ninth row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the tenth row of the 32×32 matrix have the arrangement [12341234 21432143 32143214 21432143], those in the eleventh row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the twelfth row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], those in the 13th row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the 14th row of the 32×32 matrix have the arrangement [32143214 21432143 32143214 21432143], those in the 15th row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the 16th row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], those in the 17th row of the 32×32 matrix have the arrangement [12341234 23412341 12341234 23412341], those in the 18th row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the 19th row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the 20th row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the 21st row of the 32×32 matrix have the arrangement [12341234 23412341 12341234 23412341], those in the 22nd row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the 23rd row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the 24th row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the 25th row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the 26th row of the 32×32 matrix have the arrangement [32143214 21432143 32143214 21432143], those in the 27th row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the 28th row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], those in the 29th row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the 30th row of the 32×32 matrix have the arrangement [32143214 21432143 32143214 21432143], those in the 31st row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the 32nd row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], or
• b) the base elements in the first row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], those in the second row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the third row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 34123412], those in the fourth row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the fifth row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the sixth row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the seventh row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432] those in the eighth row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the ninth row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the tenth row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432], those in the eleventh row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the twelfth row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the 13th row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the 14th row of the 32×32 matrix have the arrangement [34124123 32142143 34124123 32142143], those in the 15th row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the 16th row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], those in the 17th row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], those in the 18th row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the 19th row of the 32×32 matrix have the arrangement [34124123 32142143 34124123 32142143], those in the 20th row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the 21st row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the 22nd row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the 23rd row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432], those in the 24th row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the 25th row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the 26th row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432], those in the 27th row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the 28th row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the 29th row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the 30th row of the 32×32 matrix have the arrangement [34124123 32142143 34124123 32142143], those in the 31st row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the 32nd row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], or
• c) the base elements in the first row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the second row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the third row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the fourth row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the fifth row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the sixth row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], the seventh row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the eighth row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the ninth row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the tenth row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the eleventh row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the twelfth row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 13th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 14th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 15th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 16th row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 17th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 18th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 19th row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 20th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 21st row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 22nd row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 23rd row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 24th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 25th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 26th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 27th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 28th row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 29th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 30th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 31st row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 32nd row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], or
• d) the base elements in the first row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the second row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the third row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the fourth row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the fifth row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the sixth row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the seventh row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the eighth row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], those in the ninth row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the tenth row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the eleventh row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the twelfth row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the 13th row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the 14th row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the 15th row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the 16th row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], those in the 17th row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the 18th row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the 19th row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the 20th row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the 21st row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the 22nd row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the 23rd row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the 24th row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], those in the 25th row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the 26th row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the 27th row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the 28th row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the 29th row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the 30th row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the 31st row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the 32nd row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], or
• e) the base elements in the first row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the second row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the third row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the fourth row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the fifth row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the sixth row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the seventh row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the eighth row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the ninth row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the tenth row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the eleventh row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the twelfth row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 13th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 14th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 15th row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 16th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 17th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 18th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 19th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 20th row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 21st row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 22nd row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 23rd row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 24th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 25th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 26th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 27th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 28th row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 29th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 30th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 31st row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 32nd row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321].

An integrated circuit for measuring the polarization of incident light comprising:

• polarization-sensitive sensors with different orientations of the polarization planes as base elements in four different orientations (1,2,3,4);
• and
• sensory elements, each arranged to cooperate as a structural unit with a polarization filter for one of the polarization-sensitive sensors;
• wherein the polarization-sensitive filter of the polarization-sensitive sensor arranged as a structural unit has a specific extension and orientation,
• wherein the polarization filter has lattice structures produced by lithographic methods in at least one fabrication layer,
• wherein the polarization-sensitive sensors of different orientations consist of a plurality of individual sensor elements arranged in a matrix, wherein in the integrated circuit, devices are provided which are configured to make a statement about the polarization of the incident light from the signals of the polarization-sensitive sensors,
• wherein the base elements are arranged with different orientations (1,2,3,4) in an 8×8 matrix, and
• wherein the base elements in the first row of the 8×8 matrix have the arrangement [1,2,3,4,2,1,4,3], those in the second row of the 8×8 matrix have the arrangement [4,3,2,1,3,4,1,2], those in the third row of the 8×8 matrix have the arrangement [3,4,1,2,4,3,2,1], those in the fourth row of the 8×8 matrix have the arrangement [2,1,4,3,1,2,3,4], those in the fifth row of the 8×8 matrix have the arrangement [4,3,2,1,3,4,1,2], those in the sixth row of the arrangement have the arrangement [1,2,3,4,2,1,4,3], those in the seventh row of the 8×8 matrix have the arrangement [2,1,4,3,1,2,3,4] and those in the eighth row of the 8×8 matrix have the arrangement [3,4,1,2,4,3,2,1].

An integrated circuit for measuring the polarization of incident light comprising:

• polarization-sensitive sensors with different orientations of the polarization planes as base elements in four different orientations (1,2,3,4);
• and
• sensory elements, each arranged to cooperate as a structural unit with a polarization filter for one of the polarization-sensitive sensors;
• wherein the polarization-sensitive filter of the polarization-sensitive sensor arranged as a structural unit has a specific extension and orientation,
• wherein the polarization filter has lattice structures produced by lithographic methods in at least one fabrication layer,
• wherein the polarization-sensitive sensors of different orientations consist of a plurality of individual sensor elements arranged in a matrix,
• wherein in the integrated circuit, devices are provided which are configured to make a statement about the polarization of the incident light from the signals of the polarization-sensitive sensors,
• wherein the base elements are arranged with different orientations (1,2,3,4) in a 16×16 matrix,
• wherein
• a) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,4,3,2,1,3,4,1,2,4,3,2,1,3,4], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the fourth row of the 16×16 matrix have the arrangement [2,1,3,4,1,2,4,3,2,1,3,4,1,2,4,3], those in the fifth row of the 16×16 matrix have the arrangement [3,4,2,1,4,3,1,2,3,4,2,1,4,3,1,2], those in the sixth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the seventh row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the eighth row of the 16×16 matrix have the arrangement [4,3,1,2,3,4,2,1,4,3,1,2,3,4,2,1], those in the ninth row of the 16×16 matrix have the arrangement [1,2,4,3,2,1,3,4,1,2,4,3,2,1,3,4], those in the tenth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the eleventh row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the twelfth row of the 16×16 matrix have the arrangement [2,1,3,4,1,2,4,3,2,1,3,4,1,2,4,3], those in the thirteenth row of the 16×16 matrix have the arrangement [3,4,2,1,4,3,1,2,3,4,2,1,4,3,1,2], those in the fourteenth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the fifteenth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the sixteenth row of the 16×16 matrix have the arrangement [4,3,1,2,3,4,2,1,4,3,1,2,3,4,2,1], or
• b) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,3,4,2,3,4,1,1,4,3,2,4,3,2,1], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,1,4,3,2,2,3,4,1,1,2,3,4], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,4,1,2,3,3,2,1,4,2,1,4,3], those in the fourth row of the 16×16 matrix have the arrangement [2,1,4,3,3,2,1,4,4,1,2,3,3,4,1,2], those in the fifth row of the 16×16 matrix have the arrangement [4,1,2,3,3,4,1,2,2,1,4,3,3,2,1,4], those in the sixth row of the 16×16 matrix have the arrangement [3,2,1,4,2,1,4,3,3,4,1,2,4,1,2,3], those in the seventh row of the 16×16 matrix have the arrangement [2,3,4,1,1,2,3,4,4,3,2,1,1,4,3,2], those in the eighth row of the 16×16 matrix have the arrangement [1,4,3,2,4,3,2,1,1,2,3,4,2,3,4,1], those in the ninth row of the 16×16 matrix have the arrangement [1,4,3,2,4,3,2,1,1,2,3,4,2,3,4,1], those in the tenth row of the 16×16 matrix have the arrangement [2,3,4,1,1,2,3,4,4,3,2,1,1,4,3,2], those in the eleventh row of the 16×16 matrix have the arrangement [3,2,1,4,2,1,4,3,3,4,1,2,4,1,2,3], those in the twelfth row of the 16×16 matrix have the arrangement [4,1,2,3,3,4,1,2,2,1,4,3,3,2,1,4], those in the thirteenth row of the 16×16 matrix have the arrangement [2,1,4,3,3,2,1,4,4,1,2,3,3,4,1,2], those in the fourteenth row of the 16×16 matrix have the arrangement [3,4,1,2,4,1,2,3,3,2,1,4,2,1,4,3], those in the fifteenth row of the 16×16 matrix have the arrangement [4,3,2,1,1,4,3,2,2,3,4,1,1,2,3,4], those in the sixteenth row of the 16×16 matrix have the arrangement [1,2,3,4,2,3,4,1,1,4,3,2,4,3,2,1], or
• c) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2], those in the fourth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], those in the fifth row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4], those in the sixth row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the seventh row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2], those in the eighth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], those in the ninth row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3, 4], those in the tenth row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the eleventh row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2], those in the twelfth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], those in the thirteenth row of the 16×16 matrix have the arrangement [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4], those in the fourteenth row of the 16×16 matrix have the arrangement [4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1], those in the fifteenth row of the 16×16 matrix have the arrangement [3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2], those in the sixteenth row of the 16×16 matrix have the arrangement [2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3], or
• d) the base elements in the first row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the second row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the third row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1, 3,4,1,2,4,3,2,1], those in the fourth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the fifth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the sixth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the seventh row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the eighth row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the ninth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the tenth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2,4,3,2,1,3,4,1,2], those in the eleventh row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1], those in the twelfth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the thirteenth row of the 16×16 matrix have the arrangement [4,3,2,1,3,4,1,2 4,3,2,1,3,4,1,2], those in the fourteenth row of the 16×16 matrix have the arrangement [1,2,3,4,2,1,4,3,1,2,3,4,2,1,4,3], those in the fifteenth row of the 16×16 matrix have the arrangement [2,1,4,3,1,2,3,4,2,1,4,3,1,2,3,4], those in the sixteenth row of the 16×16 matrix have the arrangement [3,4,1,2,4,3,2,1,3,4,1,2,4,3,2,1].

An integrated circuit for measuring the polarization of light comprising:

• polarization-sensitive sensors with different orientations of the polarization planes as base elements in four different orientations (1,2,3,4);
• and
• sensory elements, each arranged to cooperate as a structural unit with a polarization filter for one of the polarization-sensitive sensors;
• wherein the polarization-sensitive filter of the polarization-sensitive sensor arranged as a structural unit has a specific extension and orientation,
• wherein the polarization filter has lattice structures produced by lithographic methods in at least one fabrication layer,
• wherein the polarization-sensitive sensors of different orientations consist of a plurality of individual sensor elements arranged in a matrix, wherein in the integrated circuit, devices are provided which are configured to make a statement about the polarization of the incident light from the signals of the polarization-sensitive sensors,
• wherein the base elements are arranged with different orientations (1,2,3,4) in a 32×32 matrix,
• wherein:
• a) the base elements in the first row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 23412341], those in the second row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the third row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the fourth row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the fifth row of the 32×32 matrix have the arrangement [12341234 23412341 12341234 23412341], those in the sixth row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the seventh row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the eighth row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the ninth row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the tenth row of the 32×32 matrix have the arrangement [32143214 21432143 32143214 21432143], those in the eleventh row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the twelfth row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], those in the 13th row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the 14th row of the 32×32 matrix have the arrangement [32143214 21432143 32143214 21432143], those in the 15th row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the 16th row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], those in the 17th row of the 32×32 matrix have the arrangement [12341234 23412341 12341234 23412341], those in the 18th row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the 19th row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the 20th row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the 21st row of the 32×32 matrix have the arrangement [12341234 23412341 12341234 23412341], those in the 22nd row of the 32×32 matrix have the arrangement [43214321 14321432 43214321 14321432], those in the 23rd row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 41234123], those in the 24th row of the 32×32 matrix have the arrangement [21432143 32143214 21432143 32143214], those in the 25th row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the 26th row of the 32×32 matrix have the arrangement [32143214 21432143 32143214 21432143], those in the 27th row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the 28th row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], those in the 29th row of the 32×32 matrix have the arrangement [41234123 34123412 41234123 34123412], those in the 30th row of the 32×32 matrix have the arrangement [32143214 21432143 32143214 21432143], those in the 31st row of the 32×32 matrix have the arrangement [23412341 12341234 23412341 12341234], those in the 32nd row of the 32×32 matrix have the arrangement [14321432 43214321 14321432 43214321], or
• b) the base elements in the first row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], those in the second row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the third row of the 32×32 matrix have the arrangement [34123412 41234123 34123412 34123412], those in the fourth row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the fifth row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the sixth row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the seventh row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432] those in the eighth row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the ninth row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the tenth row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432], those in the eleventh row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the twelfth row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the 13th row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the 14th row of the 32×32 matrix have the arrangement [34124123 32142143 34124123 32142143], those in the 15th row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the 16th row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], those in the 17th row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], those in the 18th row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the 19th row of the 32×32 matrix have the arrangement [34124123 32142143 34124123 32142143], those in the 20th row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the 21st row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the 22nd row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the 23rd row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432], those in the 24th row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the 25th row of the 32×32 matrix have the arrangement [14324321 12342341 14324321 12342341], those in the 26th row of the 32×32 matrix have the arrangement [23411234 43211432 23411234 43211432], those in the 27th row of the 32×32 matrix have the arrangement [32142143 34124123 32142143 34124123], those in the 28th row of the 32×32 matrix have the arrangement [41233412 21433214 41233412 21433214], those in the 29th row of the 32×32 matrix have the arrangement [21433214 41233412 21433214 41233412], those in the 30th row of the 32×32 matrix have the arrangement [34124123 32142143 34124123 32142143], those in the 31st row of the 32×32 matrix have the arrangement [43211432 23411234 43211432 23411234], those in the 32nd row of the 32×32 matrix have the arrangement [12342341 14324321 12342341 14324321], or
• c) the base elements in the first row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the second row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the third row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the fourth row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the fifth row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the sixth row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the seventh row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the eighth row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the ninth row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the tenth row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the eleventh row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the twelfth row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 13th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 14th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 15th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 16th row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 17th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 18th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 19th row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 20th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 21st row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 22nd row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 23rd row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 24th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 25th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 26th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 27th row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 28th row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], those in the 29th row of the 32×32 matrix have the arrangement [43214321 34123412 43214321 34123412], those in the 30th row of the 32×32 matrix have the arrangement [12341234 21432143 12341234 21432143], those in the 31st row of the 32×32 matrix have the arrangement [21432143 12341234 21432143 12341234], those in the 32nd row of the 32×32 matrix have the arrangement [34123412 43214321 34123412 43214321], or
• d) the base elements in the first row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the second row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the third row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the fourth row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the fifth row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the sixth row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the seventh row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the eighth row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], those in the ninth row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the tenth row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the eleventh row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the twelfth row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the 13th row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the 14th row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the 15th row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the 16th row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], those in the 17th row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the 18th row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the 19th row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the 20th row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the 21st row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the 22nd row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the 23rd row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the 24th row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], those in the 25th row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the 26th row of the 32×32 matrix have the arrangement [43211432 43211432 43211432 43211432], those in the 27th row of the 32×32 matrix have the arrangement [34124123 34124123 34124123 34124123], those in the 28th row of the 32×32 matrix have the arrangement [21433214 21433214 21433214 21433214], those in the 29th row of the 32×32 matrix have the arrangement [41233412 41233412 41233412 41233412], those in the 30th row of the 32×32 matrix have the arrangement [32142143 32142143 32142143 32142143], those in the 31st row of the 32×32 matrix have the arrangement [23411234 23411234 23411234 23411234], those in the 32nd row of the 32×32 matrix have the arrangement [14324321 14324321 14324321 14324321], or
• e) the base elements in the first row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the second row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the third row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the fourth row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the fifth row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the sixth row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the seventh row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the eighth row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the ninth row of the 32×32 matrix have the arrangement [12342341 12342341 12342341 12342341], those in the tenth row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the eleventh row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the twelfth row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 13th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 14th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 15th row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 16th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 17th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 18th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 19th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 20th row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 21st row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 22nd row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 23rd row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 24th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 25th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 26th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 27th row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321], those in the 28th row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 29th row of the 32×32 matrix have the arrangement [43213412 43213412 43213412 43213412], those in the 30th row of the 32×32 matrix have the arrangement [12342143 12342143 12342143 12342143], those in the 31st row of the 32×32 matrix have the arrangement [21431234 21431234 21431234 21431234], those in the 32nd row of the 32×32 matrix have the arrangement [34124321 34124321 34124321 34124321].