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Self-dual constacyclic codes of length $$2^s$$ 2 s over the ring $$\mathbb {F}_{2^m}[u,v]/\langle u^2, v^2, uv-vu \rangle $$ F 2 m [ u , v ] / ⟨ u 2 , v 2 , u v - v u ⟩
Journal of Applied Mathematics and Computing ( IF 2.2 ) Pub Date : 2021-03-31 , DOI: 10.1007/s12190-021-01526-9
Hai Q. Dinh , Pramod Kumar Kewat , Sarika Kushwaha , Woraphon Yamaka

In this paper, we classify all self-dual \(\lambda \)-constacyclic codes of length \(2^s\) over the finite commutative local ring \(R_{u^2, v^2,2^m}=\mathbb {F}_{2^m}[u,v]/\langle u^2, v^2, uv-vu \rangle \) corresponding to units of the forms \(\lambda =\alpha +\gamma v+\delta uv\), \(\alpha +\beta u+\delta uv\), \(\alpha +\beta u+\gamma v+\delta uv\), where \(\alpha ,\beta ,\gamma \in \mathbb {F}^*_{2^m}\) and \(\delta \in \mathbb {F}_{2^m}\). Moreover, the Hamming distance of these \(\lambda \)-constacyclic codes are completely determined.



中文翻译:

环$$ \ mathbb {F} _ {2 ^ m} [u,v] / \ langle u ^ 2,v ^ 2,uv-vu上长度为$$ 2 ^ s $$ 2 s的自对偶固定循环码\ rangle $$ F 2 m [u,v] /⟨u 2,v 2,uv-vu⟩

在本文中,我们对有限可交换局部环\(R_ {u ^ 2,v ^ 2,2 ^ m}上所有长度为((2 ^ s \))的自对偶\(\ lambda \)-定周期码进行分类= \ mathbb {F} _ {2 ^ m} [u,v] / \ langle u ^ 2,v ^ 2,uv-vu \ rangle \)对应形式为\(\ lambda = \ alpha + \ γv + \ delta uv \)\(\ alpha + \ beta u + \ delta uv \)\(\ alpha + \ beta u + \ gamma v + \ delta uv \),其中\(\ alpha,\ beta,\ gamma \ in \ mathbb {F} ^ * _ {2 ^ m} \)\(\ delta \ in \ mathbb {F} _ {2 ^ m} \)。此外,完全确定了这些\(\ lambda \)常数编码的汉明距离。

更新日期:2021-03-31
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