On the Codes over a Semilocal Finite Ring

Dertli A., ÇENGELLENMİŞ Y., Eren Ş.

INTERNATIONAL JOURNAL OF ADVANCED COMPUTER SCIENCE AND APPLICATIONS, cilt.6, sa.10, ss.283-292, 2015 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 10
  • Basım Tarihi: 2015
  • Dergi Adı: INTERNATIONAL JOURNAL OF ADVANCED COMPUTER SCIENCE AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.283-292
  • Anahtar Kelimeler: Cyclic codes, Skew cyclic codes, Quantum codes, CYCLIC CODES, QUANTUM CODES, ALGEBRAIC STRUCTURE, CONSTACYCLIC CODES, CONSTRUCTION
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this paper, we study the structure of cyclic, quasi cyclic, constacyclic codes and their skew codes over the finite ring R. The Gray images of cyclic, quasi cyclic, skew cyclic, skew quasi cyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The parameters of quantum error correcting codes are obtained from both cyclic and negacyclic codes over R. Some examples are given. Firstly, quasi constacyclic and skew quasi constacyclic codes are introduced. By giving two inner product, it is investigated their duality. A sufficient condition for 1 generator skew quasi constacyclic codes to be free is determined.