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$(1+2u)$-constacyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$ (1504.03445v1)
Published 14 Apr 2015 in math.RA, cs.IT, and math.IT
Abstract: Let $R=\mathbb{Z}4+u\mathbb{Z}_4,$ where $\mathbb{Z}_4$ denotes the ring of integers modulo $4$ and $u2=0$. In the present paper, we introduce a new Gray map from $Rn$ 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.
- Mohammad Ashraf (4 papers)
- Ghulam Mohammad (2 papers)