ON QUANTUM CODES FROM CYCLIC CODES OVER A CLASS OF NONCHAIN RINGS


SARI M. , Siap I.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.53, no.6, pp.1617-1628, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.4134/bkms.b150544
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1617-1628
  • Keywords: quantum codes, cyclic codes, gray map, STABILIZER CODES

Abstract

In this paper, we extend the results given in [3] to a nonchain ring R-p = F-p + vF(p) + ... + v(p-1)F(p), where v(p) = v and p is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring Rp and study the structure of their duals. We classify cyclic codes containing their duals over Rp by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map 7 defined in [4], we give the parameters of the quantum codes of length pn over F-p which are obtained from cyclic codes over R-p. Finally, we illustrate the results by giving some examples.