Data encoding methods, data decoding methods, data reconstruction methods, data encoding devices, data decoding devices, and data reconstruction devices

A data decoding method, comprising:

• inputting a plurality of encoded data items;
• determining a polynomial that corresponds to the encoded data items based on a pre-defined similarity criterion so that an evaluation of the polynomial at a sum of a first supporting point of the polynomial and a second supporting point of the polynomial corresponds to the sum of an evaluation of the polynomial at the first supporting point and an evaluation of the polynomial at the second supporting point;
• determining coefficients of the polynomial;
• and
• generating decoded data based on the coefficients.

A data encoding device, comprising:

• an input circuit configured to input data to be encoded;
• a polynomial determining circuit configured to determine a polynomial so that an evaluation of the polynomial at a sum of a first supporting point of the polynomial and a second supporting point of the polynomial corresponds to the sum of an evaluation of the polynomial at the first supporting point and an evaluation of the polynomial at the second supporting point, wherein the coefficients of the polynomial are determined based on the data to be encoded;
• and
• a generating circuit configured to generate a plurality of encoded data items by evaluating the polynomial at a plurality of supporting points.

A data decoding device, comprising:

• an input circuit configured to input a plurality of encoded data items;
• a polynomial determining circuit configured to determine a polynomial that corresponds to the encoded data items based on a pre-defined similarity criterion so that an evaluation of the polynomial at a sum of a first supporting point of the polynomial and a second supporting point of the polynomial corresponds to the sum of an evaluation of the polynomial at the first supporting point and an evaluation of the polynomial at the second supporting point;
• a coefficients determining circuit configured to determine coefficients of the polynomial;
• and
• a decoded data generating circuit configured to generate decoded data based on the coefficients.