On Z(2)Z(4)[xi]-skew cyclic codes

Gursoy F., Aydoğdu İ.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, cilt.68, sa.3, ss.1613-1633, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 68 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s12190-021-01580-3
  • Dergi Adı: JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1613-1633
  • Anahtar Kelimeler: Z(2)Z(4)-additive codes, Skew cyclic codes, Z(2)Z(4)[xi]-skew cyclic codes, Gray map, Homogeneous weight, SKEW CONSTACYCLIC CODES
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Z(2)Z(4)-additive codes have been defined as a subgroup of Zr-2 xZ(4)(s) in [6] where Z(2), Z(4) are the rings of integers modulo 2 and 4 respectively and r and s are positive integers. In this study, we define a family of codes over the set Z(2)[(xi) over bar](r) x Z(4)[xi](s) where xi is a root of a monic basic primitive polynomial in Z(4)[x]. We give the standard form of the generator and parity-check matrices of codes over Z(2)[(xi) over bar](r) x Z(4)[xi](s) and also we introduce skew cyclic codes and their spanning sets. Moreover, we study the Gray images of codes over both Z(4)[xi] and Z(2)[(xi) over bar](r) x Z(4)[xi](s) with respect to homogeneous weight and give the necessary and sufficient condition for their Gray images to be a linear code. We further present some examples of optimal codes which are actually Gray images of skew cyclic codes.