4-Cycle Free LDPC Codes Based on Difference Sets.

Difference sets are used to give a novel method for constructing structured regular quasi-cyclic low-density parity-check codes. Let Fq be a field with q elements and assume that D={d1,..., dk} is a (v,k,1)-difference set for Zv with d1<;d2<;...<;dk. Depending on v=q-1, v≥ 2dk or v≥ 2dk-1, three code construction methods are given that produce regular 4-cycle free codes, that is codes with girth a...