New constructions of entanglement-assisted quantum codes

Allahmadi A., AlKenani A., Hijazi R., Muthana N., ÖZBUDAK F., Solé P.

Cryptography and Communications, vol.14, no.1, pp.15-37, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1007/s12095-021-00499-7
  • Journal Name: Cryptography and Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Page Numbers: pp.15-37
  • Keywords: Entanglement-assisted quantum error correcting codes, Hull of a code, Concatenation, Isometry codes, LCD CODES
  • Middle East Technical University Affiliated: Yes

Abstract

© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.We present two new constructions of entanglement-assisted quantum error-correcting codes using some fundamental properties of (classical) linear codes in an effective way. The main ideas include linear complementary dual codes and related concatenation constructions. Numerical examples in modest lengths show that our constructions perform better than known constructions in the literature. We also give a proof on a generalization of binary Singleton type bound on entanglement-assisted quantum error-correcting codes to arbitrary q-ary entanglement-assisted quantum error-correcting codes.