Linear codes over F-2 x (F-2 + vF(2)) and the MacWilliams identities

ÇALIŞKAN F., Aksoy R.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, cilt.31, sa.2, ss.135-147, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00200-019-00397-9
  • Dergi Adı: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.135-147
  • Anahtar Kelimeler: Gray map, Dual code, Weight enumerator, CONSTACYCLIC CODES, CYCLIC CODES
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this work, we study linear codes over the ring F-2 x (F-2 + vF(2)) and their weight enumerators, where v(2) = v. We first give the structure of the ring and investigate linear codes over this ring. We also define two weights called Lee weight and Gray weight for these codes. Then we introduce two Gray maps from F-2 x (F-2 + vF(2)) to F-2(3) and study the Gray images of linear codes over the ring. Moreover, we prove MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators.