Non-Binary Quantum Codes from Cyclic Codes over Fp× (Fp+ vFp)

ÇALIŞKAN F., Yıldırım T., Aksoy R.

International Journal of Theoretical Physics, vol.62, no.2, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s10773-023-05294-z
  • Journal Name: International Journal of Theoretical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Keywords: Cyclic codes, Generator polynomials, Quantum codes
  • Istanbul University Affiliated: Yes

Abstract

© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.In this paper, we study cyclic codes over the ring Fp× (Fp+ vFp) , where p is an odd prime and v2 = v. We first investigate the properties of the ring Fp× (Fp+ vFp) and the linear codes over this ring. We also define a distance-preserving Gray map from Fp× (Fp+ vFp) to Fp3. We discuss cyclic codes and their dual codes over the ring. Also, we define a set of generators for these codes. As an implementation, we show that quantum error-correcting codes can be obtained from dual containing cyclic codes over the ring by using the Calderbank-Shor-Steane (CSS) construction. Furthermore, we give some illustrative examples. Finally, we tabulate the non-binary quantum error-correcting codes obtained from cyclic codes over the ring.