Entanglement-assisted binary quantum codes from skew cyclic codes over F2× (F2+ vF2)


ÇALIŞKAN F., Aksoy R., Aydin N., Liu P.

Quantum Information Processing, vol.22, no.5, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.1007/s11128-023-03945-y
  • Journal Name: Quantum Information Processing
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Compendex, INSPEC, zbMATH
  • Keywords: Dual codes, Generator polynomials, Quantum codes, Skew cyclic codes
  • Istanbul University Affiliated: Yes

Abstract

In the current paper, we study skew cyclic codes over the ring S: = F2× (F2+ vF2) with v2= v . We investigate the structural properties of skew cyclic codes over the ring S . Also, we describe the dual codes of skew cyclic codes with respect to the Euclidean inner product and the Hermitian inner product. Furthermore, we give a necessary and sufficient condition for a skew cyclic code over S to contain its dual. Using these results, we show that binary quantum error-correcting codes as well as entanglement-assisted quantum error-correcting codes can be constructed from skew cyclic codes over S . Finally, we give examples of binary entanglement-assisted quantum error-correcting codes with good parameters from skew cyclic codes over S .