Method and data processing device for determining an error vector in a data word

A data processing device for increasing data word correctability of a corrupted data word beyond a threshold of half a minimum distance of a code minus one using linear recursion syndrome determination, the data processing device comprising:

• a syndrome determination circuit configured to receive the data word, wherein n is a length of the received data word, and k is a dimension of the code as determined by n=2k−1 and determine a syndrome, the syndrome comprising a first 2k−1−k sequence elements of the received data word and a second 2k−1−k elements derived according to a linear recursion formula;
• a decoding circuit configured to successively generate code words by selecting each of a first 2k−1−k elements to be either 0 or 1 and calculating a next n−2k−1−k elements using a linear recursion formula;
• to form, for each code word generated, a sum of the syndrome supplemented with zeros to the data word length and the code word, and to check, for the code word, whether the sum of the syndrome supplemented with zeros to the data word length and the code word has a minimum weight among all code words;
• and
• an output circuit configured to output the sum of the syndrome and the code word, for which the sum of the syndrome supplemented with zeros to the data word length and the code word has a minimum weight among all code words, as the error vector;
• wherein the data word is corrected using the error vector;
• wherein the minimum distance of the code is a smallest Hamming distance between two code words.