Emergent Mind
$(1+2u)$-constacyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$
(1504.03445)
Published Apr 14, 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.
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