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Paper   IPM / M / 8792
School of Mathematics
  Title:   On full-rank paricity-check matrices of product codes
  Author(s):  M. Esmaeili
  Status:   To Appear
  Journal: Utilitas Math.
  Supported by:  IPM
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 AB. 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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