Structure and performance of generalized quasi-cyclic codes

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Guneri C., ÖZBUDAK F., Ozkaya B., Sacikara E., SEPASDAR Z., SOLÉ P.

FINITE FIELDS AND THEIR APPLICATIONS, vol.47, pp.183-202, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47
  • Publication Date: 2017
  • Doi Number: 10.1016/j.ffa.2017.06.005
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.183-202
  • Keywords: GQC codes, QC codes, LCD codes, Self-dual codes, ALGEBRAIC STRUCTURE
  • Middle East Technical University Affiliated: Yes

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. (C) 2017 Elsevier Inc. All rights reserved.