Constacyclic Codes of Arbitrary Length over $F_{q}+uF_{q}+cdots +u^{e-1}F_{q}$

Abstract

In this article, we shall study the structure of $(a+bu)-$constacyclic codes of arbitrary length over the ring<br />$R=F_{q}+uF_{q}+cdots +u^{e-1}F_{q}$, where $u^{e}=0$, $q$ is a power of a prime number $p$ and $a,b$ are non-zero elements of $F_{q}$. Also we shall find a minimal spanning set for these codes. %, and completely determine the structure of these codes. For a constacyclic code $C$ we shall determine its minimum Hamming distance with some properties of $Tor(C)$ as an $a-$constacyclic code over $F_{q}$.