Error-correction encoding and decoding

A data encoding method, comprising:

• storing, by a processing device, K input data symbols;
• assigning the K input data symbols to respective symbol locations in a notional square array, having n rows and n columns of symbol locations, to define a plurality of k-symbol words in respective rows of the array;
• encoding the k-symbol words by encoding rows and columns of the array in dependence on a product code C having identical row and column codes, each being a reversible error-correction code of dimension k and length n=2n′, thereby to define a codeword, having n2 code symbols corresponding to respective locations of the array, of a quarter product code CQ defined by CQ={X−XT−(X−XT)F:
• X∈C} where X is an (n by n)-symbol matrix defining a codeword of the product code C, XT is the transpose matrix of X, and (X−XT)F is a reflection of matrix (X−XT) in the anti-diagonal thereof;
• and
• outputting to a data channel the n′(n′−1) code symbols in the codeword of CQ which correspond to respective locations in a triangular subarray confined between the diagonal and anti-diagonal of the array.