QUANTUM CODES OVER A CLASS OF FINITE CHAIN RINGS

SARI M., Siap I.

QUANTUM INFORMATION & COMPUTATION, cilt.16, ss.39-49, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16
  • Basım Tarihi: 2016
  • Dergi Adı: QUANTUM INFORMATION & COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.39-49
  • Anahtar Kelimeler: Quantum codes, Cylic codes, Gray map
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this study, we introduce a new Gray map which preserves the orthogonality from the chain ring F-2 [u] / (u(s)) to F-2(s) where F-2 is the finite field with two elements. We also give a condition of the existence for cyclic codes of odd length containing its dual over the ring F-2 [u] / (u(s)). By taking advantage of this Gray map and the structure of the ring, we obtain two classes of binary quantum error correcting (QEC) codes and we finally illustrate our results by presenting some examples with good parameters.