Some results on the linear codes over the finite ring F-2 + v(1)F(2) + ... + v(r)F(2)

Dertli A., ÇENGELLENMİŞ Y., Eren Ş.

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, cilt.14, sa.1, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s021974991650012x
  • Dergi Adı: INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Quantum codes, cyclic codes, skew codes, finite rings, CYCLIC CODES, ALGEBRAIC STRUCTURE, QUANTUM CODES, CONSTRUCTION
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this paper, we study the structure of cyclic, quasi-cyclic codes and their skew codes over the finite ring B-r = F-2 + v(1)F(2) + ... + v(r)F(2), v(i)(2) + v(i), v(i)v(j) = v(j)v(i) 0, 1 <= i, j <= r for r >= 1. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic codes over B-r are obtained. A necessary and sufficient condition for cyclic code over Br that contains its dual has been given. The parameters of quantum error correcting codes are obtained from cyclic codes over B-r.