A study on constacyclic codes over the ring \mathbb{Z}_۴+u\mathbb{Z}_۴+u^۲\mathbb{Z}_۴

This paper studies \lambda-constacyclic codes and skew \lambda-constacyclic codes over the finite commutative non-chain ring R=\mathbb{Z}_۴+u\mathbb{Z}_۴+u^۲\mathbb{Z}_۴ with u^۳=۰ for \lambda= (۱+۲u+۲u^۲) and (۳+۲u+۲u^۲). We introduce distinct Gray maps and show that the Gray images of \lambda-constacyclic codes are cyclic, quasi-cyclic, and permutation equivalent to quasi-cyclic codes over \mathbb{Z}_۴. It is also shown that the Gray images of skew \lambda-constacyclic codes are quasi-cyclic codes of length ۲n and index ۲ over \mathbb{Z}_۴. Moreover, the structure of \lambda-constacyclic codes of odd length n over the ring R is determined and give some suitable examples.

کلیدواژه ها:

constacyclic code ، Cyclic code ، Gray map ، quasi-cyclic code ، skew constacyclic code