An application of constacyclic codes to entanglement-assisted quantum MDS codes


Creative Commons License

Sarı M. , Kolotoğlu E.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.38, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38
  • Publication Date: 2019
  • Doi Number: 10.1007/s40314-019-0837-1
  • Title of Journal : COMPUTATIONAL & APPLIED MATHEMATICS
  • Keywords: Entanglement-assisted quantum codes, Constacyclic codes, Defining sets, DISTANCE

Abstract

The constructions of entanglement-assisted quantum codes have been studied intensively by researchers. Nevertheless, it is hard to determine the number of shared pairs required for constructing entanglement-assisted quantum codes from linear codes. In this paper, by making use of the notion of decomposition for defining sets of constacyclic codes, we construct several new families of entanglement-assisted quantum MDS codes from constacyclic codes, some of which are of minimum distances greater than q + 1. Moreover, we tabulate their parameters to illustrate what we find in this paper.