Given fullrank paritycheck matrices H_{A} and
H_{B} for linear binary codes A and
B, respectively, two fullrank paritycheck matrices,
denoted H_{1} and H_{2}, are given for the product code
A⊗B. It is shown that the girth of
Tanner graph TG(H_{i}) associated with H_{i}, i = 1,2, is
bounded below by {g_{a}, g_{b}, 8} where g_{a} and g_{b}
are the girths of TG(H_{A}) and TG(H_{B}),
respectively. It turns out that the product of m ≥ 2 single
paritycheck codes is either cyclefree or has girth 8, and a
necessary and sufficient condition for having the latter case is
provided.
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