Z(2)Z(2)[u]-Cyclic and Constacyclic Codes

Aydoğdu İ., Abualrub T., Siap I.

IEEE TRANSACTIONS ON INFORMATION THEORY, cilt.63, ss.4883-4893, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1109/tit.2016.2632163
  • Dergi Adı: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4883-4893
  • Anahtar Kelimeler: Linear codes, cyclic codes, constacyclic codes, Z(2)Z(2)[u]-linear cyclic codes, duality, bounds, CYCLIC CODES, RINGS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Following the very recent studies on Z(2)Z(4)-additive codes, Z(2)Z(2)[u]-linear codes have been introduced by Aydogdu et al. In this paper, we introduce and study the algebraic structure of cyclic, constacyclic codes and their duals over the R-module Z(2)(alpha)R(beta) where R = Z(2)+uZ(2) = {0, 1, u, u + 1} is the ring with four elements and u(2) = 0. We determine the generating independent sets and the types and sizes of both such codes and their duals. Finally, we present a bound and an optimal family of codes attaining this bound and also give some illustrative examples of binary codes that have good parameters which are obtained from the cyclic codes in Z(2)(alpha)R(beta).