On the linear codes over the ring R-p

Dertli A., ÇENGELLENMİŞ Y., Eren Ş.

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, vol.8, no.2, 2016 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1142/s1793830916500361
  • Journal Name: DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Keywords: Quantum codes, cyclic codes, skew codes, finite rings, CYCLIC CODES, ALGEBRAIC STRUCTURE, CONSTACYCLIC CODES, QUANTUM CODES, CONSTRUCTION
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Some results are generalized on linear codes over Z(3)[v]/< v(3) - v > in [15] to the ring R-p = Z(p)[v]/< v(p) - v >, where p is an odd prime number. The Gray images of cyclic and quasi-cyclic codes over R-p are obtained. The parameters of quantum error correcting codes are obtained from negacyclic codes over R-p. A nontrivial automorphism theta(p) on the ring R-p is determined. By using this, the skew cyclic, skew quasi-cyclic, skew constacyclic codes over R-p are introduced. The number of distinct skew cyclic codes over R-p is given. The Gray images of skew codes over R-p are obtained. The quasi-constacyclic and skew quasi-constacyclic codes over R-p are introduced. MacWilliams identities of linear codes over R-p are given.