Constacyclic Codes of Arbitrary Length over F_{q}+uF_{q}+\cdots +u^{e-۱}F_{q}

In this article, we shall study the structure of (a+bu)-constacyclic codes of arbitrary length over the ringR=F_{q}+uF_{q}+\cdots +u^{e-۱}F_{q}, where u^{e}=۰, 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}.

Keywords:

Linear code , constacyclic code , minimal spanning set , minimum Hamming distance