Skew Cyclic Codes Over Z4+uZ4+u2Z4 with Derivation and New Z4 Codes

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Şahinkaya S., Caliskan B., Ustun D., Sharma A., Eskal C.

Bulletin of the Malaysian Mathematical Sciences Society, cilt.49, sa.2, 2026 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 49 Sayı: 2
• Basım Tarihi: 2026
• Doi Numarası: 10.1007/s40840-026-02050-4
• Dergi Adı: Bulletin of the Malaysian Mathematical Sciences Society
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
• Anahtar Kelimeler: 94B05, 94B60, Cyclic codes, derivation, Gray map, skew cyclic codes
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we study a class of skew-cyclic codes over the ring R=Z4+uZ4+u2Z4, where u3=0 with an automorphism θ and a derivation δθ and we call such codes: δθ-cyclic codes. Some structural properties of the skew polynomial ring R[x,θ,δθ] are discussed and these codes are considered as left R[x,θ,δθ]-submodules. Generator and parity-check matrices of a free δθ-cyclic code of even length over R are determined. A Gray map on R is used to obtain the Z4-images. Furthermore, these codes are generalized to double skew-cyclic codes. As an application of δθ-cyclic codes, we have obtained new quaternary linear codes from the Gray images of δθ-cyclic codes over R and added them to Aydin’s codetable.