m-ADIC RESIDUE CODES OVER THE RING F-q[v]/(v(s) - v) AND THEIR APPLICATIONS TO QUANTUM CODES

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Kuruz F., Sarı M., Köroğlu M. E.

QUANTUM INFORMATION & COMPUTATION, cilt.22, sa.5-6, ss.427-439, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 5-6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.26421/qic22.5-6-4
  • Dergi Adı: QUANTUM INFORMATION & COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.427-439
  • Anahtar Kelimeler: m-adic residue codes, Cyclic codes, Quadratic residue codes, CSS construction, Quantum codes, CYCLIC CODES
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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-q[v]/< v(s)-v >. We determine the idempotent generators of the m-adic residue codes over F-q[v]/< v(s)-v >. We obtain some parameters of optimal m-adic residue codes over F-q[v]/< v(s)-v > with respect to Griesmer bound for rings. Furthermore, we derive a condition for m-adic residue codes over F-q [v]/< v(s)-v > 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 F-q[v]/< v(s)-v > and give some examples to illustrate our findings.