Construction of binary minimal product parity-check matrices
`A parity-check matrix H of a given code C is called minimal if it has minimum number of nonzero entries among all parity-check matrices representing C. Let C-1 and C-2 be two binary linear block codes with minimal parity-check matrices H-1 and H-2, respectively. It is shown that, using H-1 and H2, one can efficiently generate a minimal parity-check matrix for the product code C-1 circle times C-2.
minimal parity-check matrices product codes