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

ÇALIŞKAN F., Aksoy R.

Filomat, vol.37, no.15, pp.5137-5147, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 15
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2315137c
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.5137-5147
  • Keywords: Cyclic code, Dual code, Generator polynomial, Quantum code
  • Istanbul University Affiliated: Yes

Abstract

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).