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
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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.
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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.
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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.
Dertli, A. (2020). Skew lamda-cyclic Codes over Y_2. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 13 Sayı: ÖZEL SAYI I Özel Sayı, 92–96. https://doi.org/10.18185/erzifbed.635690
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