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

Document Type : Research Paper


1 Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran

2 Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71467-13565, Iran.


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 $F_{q}$.


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