A parity-check matrix
H of a given code
C{\mathcal{C}} is called minimal if it has minimum number of nonzero entries among all parity-check matrices representing
C{\mathcal{C}} . Let
C1{\mathcal{C}_1} and
C2{\mathcal{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
H
2, one can efficiently generate a minimal parity-check matrix for the product code
C1ÄC2{\mathcal{C}_1\otimes\mathcal{C}_2} .
Keywords Product codes - Minimal parity-check matrices