title: (1 + u)-Constacyclic codes over Z 4 + uZ 4.
abstract: Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z 4 + uZ 4 of any length are studied. A new Gray map between Z 4 + uZ 4 and Z 4 (4) is defined. By means of this map, it is shown that the Z 4 Gray image of a (1 + u)-constacyclic code of length n over Z 4 + uZ 4 is a cyclic code over Z 4 of length 4n. Furthermore, by combining the classical Gray map between Z 4 and F 2 (2), it is shown that the binary image of a (1 + u)-constacyclic code of length n over Z 4 + uZ 4 is a distance invariant binary quasi-cyclic code of index 4 and length 8n. Examples of good binary codes are constructed to illustrate the application of this class of codes.
authors: Department of Mathematics and Physics, Hefei University, Hefei, China.
authors: Haifeng
authors: H
authors: Yu
authors: Department of Mathematics and Physics, Hefei University, Hefei, China.
authors: Yu
authors: Y
authors: Wang
authors: School of Mathematical Sciences, Anhui University, Hefei, China.
authors: Minjia
authors: M
authors: Shi
keywords: Constacyclic code; Cyclic code; Gray map; Quasi-cyclic code