CYCLIC AND SKEW CYCLIC CODES OVER THE F-q

Dertli A., ÇENGELLENMİŞ Y.

JOURNAL OF SCIENCE AND ARTS, sa.1, ss.13-22, 2016 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2016
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.13-22
  • Anahtar Kelimeler: Cyclic code, skew cyclic code, finite ring, CONSTRUCTION
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this paper, we study the structure of cyclic and skew cyclic codes over the finite ring D-k = F-q +v(1)F(q) + ... v(k)F(q), v(i)(2) = v(i), v(i)v(j) = v(j)v(i) = 0, 1 <= i, j <= k, q = p(m), p is a prime for k >= 1 which contains the ring F-q + v(1)F(q), v(1)(2) = v(1). We define a new Gray map from D-k to F-q(k+1). The algebraic structures of cyclic codes and duality properties are investigated. A linear code over D-k is represented by means of k+1 q-ary codes. The non trivial automorphism over D-k is given and the skew cyclic codes over D-k are introduced. The algebraic structure of skew cyclic codes and duality properties are investigated. The Gray images of both cyclic and skew cyclic codes over D-k are obtained.