Skew lamda-cyclic Codes over Y_2

Year 2020, , 92 - 96, 28.02.2020

Abdullah Dertli , Yasemin Çengellenmiş

https://doi.org/10.18185/erzifbed.635690

Abstract

In the
present paper, by defining two non-trivial automorphisms and Gray maps over Y_2=Z_4+uZ_4+vZ_4+uvZ_4 where  u^2=0,v^2=0,uv=vu , the algebraic structcure of the skew lamda-cyclic codes and their  Gray images over the finite ring Y_2 are determined, where  a=1+u+v+uv.

Keywords

Skew codes, Gray map, Finite rings

Supporting Institution

-

Y_2 Halkası Üzerinde Skew lama-cyclic Kodlar

Abstract

Bu çalışmada, u^2=0,v^2=0,uv=vu, lamda=1+u+v+uv, olmak üzere  Y_2=Z_4+uZ_4+vZ_4+uvZ_4,sonlu halkası üzerinde iki farklı Gray
dönüşümü ve otomorfizma tanımlanarak skew lamda-cyclic kodların cebirsel yapısı ve bu kodların Gray
görüntüleri belirlenmiştir.

Keywords

Skew kodlar, Gray dönüşümü, Sonlu halkalar

References

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• Boucher D., Willi G., Ulmer F. 2007. “Skew cyclic codes”, Applicable Algebra in Engineering, Communication and Computing, 17, 379-389.
• Boucher D., Sole P., Ulmer F. 2008. “Skew constacyclic codes over Galois rings”, Advances in mathematics of communications, 3, 273-292.
• Dertli A., Cengellenmis Y., Eren S. 2015. On “Skew Cyclic and Quasi-cyclic Codes over ”, Palestine Journal of Mathematics, 4, 540-546.