Structure and performance of generalized quasi-cyclic codes

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2017-09-01

Author

Guneri, Cem
Özbudak, Ferruh
Ozkaya, Buket
Sacikara, Elif
SEPASDAR, Zahra
SOLÉ, Patrick

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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.

Subject Keywords

GQC codes, QC codes, LCD codes, Self-dual codes

URI

https://hdl.handle.net/11511/39871

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2017.06.005

Collections

Department of Mathematics, Article

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Citation Formats

C. Guneri, F. Özbudak, B. Ozkaya, E. Sacikara, Z. SEPASDAR, and P. SOLÉ, “Structure and performance of generalized quasi-cyclic codes,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 183–202, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39871.