F2F4-skew cyclic codes

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Hesari R. M., SARI M., AYDOĞDU İ.

Computational and Applied Mathematics, cilt.44, sa.5, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 5
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s40314-025-03226-7
  • Dergi Adı: Computational and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Anahtar Kelimeler: Cyclic codes, Mixed alphabet, Optimal codes, Skew codes
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.