@article { author = {Majdzadeh, M. and Gholami, M. and Raeisi, Gh.}, title = {(7,K) GIRTH-8 QC-LDPC CODES WITH AN EXPLICIT CONSTRUCTION}, journal = {Journal of Algebraic Systems}, volume = {9}, number = {2}, pages = {229-239}, year = {2022}, publisher = {Shahrood University of Technology}, issn = {2345-5128}, eissn = {2345-511X}, doi = {10.22044/jas.2021.8911.1434}, abstract = {Recently, for each row weight $K$ and column-weight $J$, $3\le J< K$, several classes of $(J,K)$ quasi-cyclic (QC) low-density parity-check (LDPC) codes with girth 8 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 $J=7$, a class of $(7,K)$ QC-LDPC codes with girth 8 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 $(K-1)(K^2+K)+1$.}, keywords = {QC-LDPC codes,explicit constructions,girth,exponent matrix}, url = {https://jas.shahroodut.ac.ir/article_2195.html}, eprint = {https://jas.shahroodut.ac.ir/article_2195_c0df1d88cfdf2c920bfa4dcd2111e302.pdf} }