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- W4316039465 abstract "In this article, we consider a semi-local ring S=Fq+uFq, where u2=u, q=ps and p is a prime number. We define a multiplication yb=β(b)y+γ(b), where β is an automorphism and γ is a β-derivation on S so that S[y;β,γ] becomes a non-commutative ring which is known as skew polynomial ring. We give the characterization of S[y;β,γ] and obtain the most striking results that are better than previous findings. We also determine the structural properties of 1-generator skew cyclic and skew-quasi cyclic codes. Further, We demonstrate remarkable results of the above-mentioned codes over S. Finally, we find the duality of skew cyclic and skew-quasi cyclic codes using a symmetric inner product. These codes are further generalized to double skew cyclic and skew quasi cyclic codes and a table of optimal codes is calculated by MAGMA software." @default.
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- W4316039465 date "2023-01-13" @default.
- W4316039465 modified "2023-10-18" @default.
- W4316039465 title "(β,γ)-Skew QC Codes with Derivation over a Semi-Local Ring" @default.
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- W4316039465 doi "https://doi.org/10.3390/sym15010225" @default.
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