New Entanglement-Assisted Quantum MDS Codes with Maximal Entanglement

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SARI M., KÖROĞLU M. E.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, vol.60, no.1, pp.243-253, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s10773-020-04682-z
  • Journal Name: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Page Numbers: pp.243-253
  • Keywords: Entanglement-assisted quantum codes, Constacyclic codes, Linear complementary dual codes, Hermitian construction, Defining sets
  • Yıldız Technical University Affiliated: Yes

Abstract

The construction of maximum distance separable (MDS) linear complementary dual (LCD) codes and entanglement-assisted quantum MDS (EAQMDS) codes have been of a great interest. In this paper, for arbitrary prime power q, we construct two new families of MDS Hermitian LCD codes of length n = q(2)+1/lambda and n = q(2)-1/ r, where rq + 1. By applying the obtained MDS Hermitian LCD codes to the EAQMDS codes, we derive new maximal entanglement EAQMDS codes of parameters [[q(2)+1/lambda, q(2)+1/lambda - l + 1, l; l - 1]](q) where 2 <= l left perpendicular <= q(2)+1+2 lambda/2 lambda right perpendicular and [[q(2)-1/r, q(2)-1/r - gamma, gamma + 1; gamma]](q) where 1 <= gamma <= q(2)-1/2r