2017/02/01 by Güneri, Cem, Özbudak, Ferruh, Özkaya, Buket +3
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1702.00153
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.