Cyclic codes over F2 × (F2 + vF2) and binary quantum codes

ÇALIŞKAN F., Aksoy R.

Filomat, cilt.37, sa.15, ss.5137-5147, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 15
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2298/fil2315137c
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.5137-5147
  • Anahtar Kelimeler: Cyclic code, Dual code, Generator polynomial, Quantum code
  • İstanbul Üniversitesi Adresli: Evet

Özet

In the present study, we define cyclic codes over the commutative principal ideal ring F2 × (F2 + vF2) with v2 = v and obtain some results on cyclic codes over F2 × (F2 + vF2). We also investigate the dual of a cyclic code over F2 × (F2 + vF2) depending on two inner products. We determine a generator polynomial of cyclic codes and give the calculation of the number of cyclic codes over F2 × (F2 + vF2). Furthermore, we show that the Gray images of a cyclic code over F2 × (F2 + vF2) of length n are binary quasi-cyclic codes of length 3n and of index 3. We find numerous binary codes as Gray images of cyclic codes over F2 × (F2 + vF2) and tabulate the optimal ones. Moreover, we show that it is possible to obtain binary quantum error-correcting codes (QECCs) from cyclic codes over F2 × (F2 + vF2).