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| Paper IPM / M / 8792 |
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| Abstract: | |
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Given full-rank parity-check matrices HA and
HB for linear binary codes A and
B, respectively, two full-rank parity-check matrices,
denoted H1 and H2, are given for the product code
A⊗B. It is shown that the girth of
Tanner graph TG(Hi) associated with Hi, i = 1,2, is
bounded below by {ga, gb, 8} where ga and gb
are the girths of TG(HA) and TG(HB),
respectively. It turns out that the product of m ≥ 2 single
parity-check codes is either cycle-free or has girth 8, and a
necessary and sufficient condition for having the latter case is
provided.
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