New q-ary quantum MDS codes of length strictly larger than q+1

Kırcalı M., ÖZBUDAK F.

Quantum Information Processing, vol.23, no.12, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 12
  • Publication Date: 2024
  • Doi Number: 10.1007/s11128-024-04598-1
  • Journal Name: Quantum Information Processing
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Compendex, INSPEC, zbMATH
  • Keywords: Hermitian self-orthogonal code, Quantum MDS codes, Reed-Solomon code, Truncated code
  • Middle East Technical University Affiliated: Yes

Abstract

Quantum information and quantum computation have become a hot topic in recent decades. Quantum error-correcting codes are useful and have many applications in quantum computations and quantum communications. We construct a new class of quantum Maximum Distance Separable (MDS) codes. Our construction is based on a recent result of Ball and Vilar (IEEE Trans Inf Theory 68:3796–3805, 2022). We study a large class of explicit polynomials and obtain their required arithmetical properties which imply construction of new q-ary quantum MDS codes of length strictly larger than q+1, when q is odd.