Improved Spectral Bound for Quasi-Cyclic Codes

Luo G., Ezerman M. F., Ling S., Özkaya B.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.70, no.6, pp.4002-4015, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 6
  • Publication Date: 2024
  • Doi Number: 10.1109/tit.2024.3364489
  • Journal Name: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.4002-4015
  • Keywords: minimum distance, Quasi-cyclic code, spectral bound
  • Middle East Technical University Affiliated: Yes

Abstract

Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the corresponding eigenspaces, we provide an improved spectral bound for quasi-cyclic codes. Numerical results verify that the improved bound outperforms the Jensen bound in almost all cases. Based on the improved bound, we propose a general construction of quasi-cyclic codes with excellent designed minimum distances. For the quasi-cyclic codes produced by this general construction, the improved spectral bound is always sharper than the Jensen bound.