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arXiv · 1702.00153

Structure and Performance of Generalized Quasi-Cyclic Codes

Cem Güneri·Ferruh Özbudak·Buket Özkaya·Elif Saçıkara·Zahra Sepasdar·Patrick Solé
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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.

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Cem Güneri, Ferruh Özbudak, Buket Özkaya, Elif Saçıkara, Zahra Sepasdar, Patrick Solé. 2017-02-01. Structure and Performance of Generalized Quasi-Cyclic Codes. https://arxiv.org/abs/1702.00153

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