Z_8+uZ_8 Halkası Üzerinde Çift Aykırı Devirli Kodlar

Abstract

Bu çalışmada u^2=1 olmak üzere 〖S=Z〗_8+uZ_8 halkası üzerindeki aykırı devirli ve çift (double) aykırı devirli kodlar çalışılmıştır. θ, S üzerinde bir otomorfizm ve δ_θ S üzerinde bir türetim (derivation) olmak üzere S[x,θ,δ_θ ] aykırı polinomlar halkası tanımlanmıştır. S üzerinde δ_θ-devirli kodlar tanımlanarak bu kod ailesinin bazı cebirsel özellikleri incelenmiştir. Ayrıca bu kod sınıfının bir genellemesi olan çift aykırı devirli kodlar çalışılmıştır.

Keywords

• Devirli Kod
• Aykırı Polinomlar Halkası
• Aykırı Devirli Kod
• Gray Dönüşümü

Double Skew Cyclic Codes over the Ring Z_8+uZ_8

Abstract

In this work, skew cyclic and double skew cyclic codes over the ring 〖S=Z〗_8+uZ_8 where u^2=1 are studied. The skew polynomial ring S[x,θ,δ_θ ] are introduced, where θ is an automorphism on S and δ_θ is a derivation on S. Defining δ_θ-cyclic codes, some algebric properties of these families of codes are invastigated. Also, double skew cyclic codes regarding as a generalization of skew cyclic codes are studied.

Keywords

• Cyclic Code
• Skew Polinomial Ring
• Skew Cyclic Code
• Gray Map

References

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