Skew Cyclic Codes Of Arbitrary Length Over R=Fp[v]/(v^۲^k -۱)

In thise paper we study an special type of Cyclic Codes called skewCyclic codes over the ring R=Fp[v]/(v^۲^k-۱) where is a prime number. This setsOf codes are the result of module (or ring) structure of the skew polynomial ringR=[x,Q] where v^۲^k=۱ and Q is an Fp automorphism such that Q(v)=v^۲^k-۱.We show that when n is even these codes are principal and if n is odd these codeLook like a module and proof some properties.

Keywords:

skew cyclic code , Ring , code over ring