F2F4-skew cyclic codes

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Hesari R. M., SARI M., AYDOĞDU İ.

Computational and Applied Mathematics, vol.44, no.5, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 5
  • Publication Date: 2025
  • Doi Number: 10.1007/s40314-025-03226-7
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: Cyclic codes, Mixed alphabet, Optimal codes, Skew codes
  • Yıldız Technical University Affiliated: Yes

Abstract

In this study, we introduce F2F4-skew cyclic codes as a generalization of skew cyclic codes over F4. We characterize algebraic structures of F2F4-skew cyclic codes by determining their generating polynomials and minimal spanning sets. We also exhibit generator matrices for these codes. Furthermore, we examine the duals of F2F4-skew cyclic codes concerning a certain inner product and identify their generating polynomials. Finally, as an application of F2F4-skew cyclic codes, we present some examples of near-MDS codes over F4 and optimal binary linear codes which are Gray images of F2F4-skew cyclic codes.