Structure and performance of generalized quasi-cyclic codes
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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Official URL: http://dx.doi.org/10.1016/j.ffa.2017.06.005
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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