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arXiv · 1504.03445

$(1+2u)$-constacyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$

Mohammad Ashraf·Ghulam Mohammad
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Abstract

Let $R=\mathbb{Z}_4+u\mathbb{Z}_4,$ where $\mathbb{Z}_4$ denotes the ring of integers modulo $4$ and $u^2=0$. In the present paper, we introduce a new Gray map from $R^n$ to $\mathbb{Z}_{4}^{2n}.$ We study $(1+2u)$-constacyclic codes over $R$ of odd lengths with the help of cyclic codes over $R$. It is proved that the Gray image of $(1+2u)$-constacyclic codes of length $n$ over $R$ are cyclic codes of length $2n$ over $\mathbb{Z}_4$. Further, a number of linear codes over $\mathbb{Z}_4$ as the images of $(1+2u)$-constacyclic codes over $R$ are obtained.

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BibTeXRIS

Mohammad Ashraf, Ghulam Mohammad. 2015-04-14. $(1+2u)$-constacyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$. https://arxiv.org/abs/1504.03445

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