%0 Journal Article %T Constacyclic Codes of Arbitrary Length over $F_{q}+uF_{q}+\cdots +u^{e-1}F_{q}$ %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Beygi, Marziyeh %A Namazi, Shohreh %A Sharif, Habib %D 2019 %\ 03/01/2019 %V 6 %N 1 %P 65-82 %! Constacyclic Codes of Arbitrary Length over $F_{q}+uF_{q}+\cdots +u^{e-1}F_{q}$ %K Linear code %K constacyclic code %K minimal spanning set %K minimum Hamming distance %R 10.22034/as.2019.1355 %X In this article, we shall study the structure of $(a+bu)-$constacyclic codes of arbitrary length over the ring$R=F_{q}+uF_{q}+\cdots +u^{e-1}F_{q}$, 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 $F_{q}$. %U https://as.yazd.ac.ir/article_1355_8a201cea56ab8e4a73196e35893cbf91.pdf