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

Abstract: Let

R = m a t h b b Z_{4} + u m a t h b b Z_{4},

where

m a t h b b 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

m a t h b b Z_{4}^{2 n} .

We study

(1 + 2 u)

-constacyclic codes over

R

of odd lengths with the help of cyclic codes over

R

. It is proved that the Gray image of

(1 + 2 u)

-constacyclic codes of length

n

over

R

are cyclic codes of length

2 n

over

m a t h b b Z_{4}

. Further, a number of linear codes over

m a t h b b Z_{4}

as the images of

(1 + 2 u)

-constacyclic codes over

R

are obtained.

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