Skew Generalized Quasi-Cyclic Codes over Finite Fields
Information Theory
2013-09-09 v1 math.IT
Abstract
In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynomial, determine the dimension and give a lower bound on the minimum Hamming distance. The skew quasi-cyclic (QC) codes are also discussed briefly.
Cite
@article{arxiv.1309.1621,
title = {Skew Generalized Quasi-Cyclic Codes over Finite Fields},
author = {Jian Gao and Linzhi Shen and Fang-Wei Fu},
journal= {arXiv preprint arXiv:1309.1621},
year = {2013}
}
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