Structure and performance of generalized quasi-cyclic codes

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Güneri, Cem and Özbudak, Ferruh and Özkaya, Buket and Saçıkara Karıksız, Elif and Sepasdar, Zahra and Sole, Patrick (2017) Structure and performance of generalized quasi-cyclic codes. Finite Fields and Their Applications, 47 . pp. 183-202. ISSN 1071-5797 (Print) 1090-2465 (Online)

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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.
Item Type: Article
Uncontrolled Keywords: GQC codes; QC codes; LCD codes; Self-dual codes
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Cem Güneri
Date Deposited: 17 Aug 2017 15:50
Last Modified: 17 Aug 2017 15:50
URI: https://research.sabanciuniv.edu/id/eprint/32921

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