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, cilt.47, ss.183-202, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1016/j.ffa.2017.06.005
  • Dergi Adı: FINITE FIELDS AND THEIR APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.183-202
  • Anahtar Kelimeler: GQC codes, QC codes, LCD codes, Self-dual codes, ALGEBRAIC STRUCTURE
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.