M. Majdzadeh - Department of Mathematics, Shahrekord University, Shahrekord, Iran.
M. Gholami - Department of Mathematics, Shahrekord University, Shahrekord, Iran.
Gh. Raeisi - Department of Mathematics, Shahrekord University, Shahrekord, Iran.

Recently, for each row weight K and column-weight J, ۳\le J< K, several classes of (J,K) quasi-cyclic (QC) low-density parity-check (LDPC) codes with girth ۸ have been constructed explicitly such that their corresponding lower-bounds on the size of circulant permutation matrices (CPMs) have been considered small as possible. In this paper, for J=۷, a class of (۷,K) QC-LDPC codes with girth ۸ is generated by an explicit method such that the lower-bounds of the constructed codes remarkably are better than the state-of-the-art bound (K-۱)(K^۲+K)+۱.

QC-LDPC codes, explicit constructions, girth, exponent matrix