Z_8+uZ_8 Halkası Üzerinde Çift Aykırı Devirli Kodlar

Year 2021, Volume: 10 Issue: 4, 1272 - 1281, 31.12.2021

Basri Çalışkan

https://doi.org/10.17798/bitlisfen.904152

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

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