Structure and Performance of Generalized Quasi-Cyclic Codes
Information Theory
2017-02-02 v1 math.IT
Abstract
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of concatenated codes. This decomposition leads to a trace formula, a minimum distance bound, and to a criteria for the GQC code to be self-dual or to be linear complementary dual (LCD). Explicit long GQC codes that are LCD, but not QC, are exhibited.
Cite
@article{arxiv.1702.00153,
title = {Structure and Performance of Generalized Quasi-Cyclic Codes},
author = {Cem Güneri and Ferruh Özbudak and Buket Özkaya and Elif Saçıkara and Zahra Sepasdar and Patrick Solé},
journal= {arXiv preprint arXiv:1702.00153},
year = {2017}
}