m-ADIC RESIDUE CODES OVER THE RING Fq [v]/(vs - v) AND THEIR APPLICATIONS TO QUANTUM CODES

Kuruz F., SARI M., KÖROĞLU M. E.

Quantum Information and Computation, vol.22, no.5-6, pp.427-439, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 5-6
  • Publication Date: 2022
  • Doi Number: 10.26421/qic22.5-6-4
  • Journal Name: Quantum Information and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, zbMATH
  • Page Numbers: pp.427-439
  • Keywords: CSS construction, Cyclic codes, M-adic residue codes, Quadratic residue codes, Quantum codes
  • Istanbul Gelisim University Affiliated: Yes

Abstract

© Rinton Press.Due to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes. The m-adic residue codes are the generalization of the duadic codes. The aim of this paper is to study the structure of the m-adic residue codes over the quotient ring -F-vy. We determine the idempotent generators of the m-adic residue codes over -^—j. We obtain some parameters of optimal m-adic residue codes over -^—vy with respect to Griesmer bound for rings. Furthermore, we derive a condition for m-adic residue codes over -§-?)' to contain their dual. By making use of a preserving-orthogonality Gray map, we construct a family of quantum error correcting codes from the Gray images of dual-containing m-adic residue codes over -§-?)' and give some examples to illustrate our findings.