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.
📌 3 Key Takeaways
🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
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.
Özet
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.
DERTLİ, A., Çengellenmiş, Y. (2020). Skew lamda-cyclic Codes over Y_2. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 13 - Sayı: ÖZEL SAYI I, 92–96. https://ajindex.com/articles/233923
Abualrub T., Seneviratne P. 2012. “On -cyclic codes over ”, Australasian Journal of Com., 54, 115-126.
Abualrub T., Ghrayeb A., Aydın N., Siap I. 2010. “On the construction of skew quasi-cyclic codes”, IEEE Transsactions on Information Theory, 56, 2081-2090.
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.