1-2hit |
Tingting WU Jian GAO Fang-Wei FU
Let R=Z4 be the integer ring mod 4 and C be a linear code over R. The code C is called a triple cyclic code of length (r, s, t) over R if the set of its coordinates can be partitioned into three parts so that any cyclic shift of the coordinates of the three parts leaves the code invariant. These codes can be viewed as R[x]-submodules of R[x]/
Minjia SHI Ting YAO Adel ALAHMADI Patrick SOLÉ
In this article, we study skew cyclic codes over $R=mathbb{F}_{q}+vmathbb{F}_{q}+v^{2}mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and v3=v. We describe the generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomial of the dual of a skew cyclic code over R. Moreover, the idempotent generators of skew cyclic codes over $mathbb{F}_{q}$ and R are considered.