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, vol.31, no.2, pp.135-147, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1007/s00200-019-00397-9
  • Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.135-147
  • Keywords: Gray map, Dual code, Weight enumerator, CONSTACYCLIC CODES, CYCLIC CODES
  • Istanbul University Affiliated: Yes

Abstract

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.