Skew Cyclic Codes Of Arbitrary Length Over $R=\frac{F_p[v]}{({v}^{{2}^{k}}-1)}$

Subject Areas : Applied Mathematics

Alireza  Soleimani ¹ (Faculty of Mathematics, Tarbiat Modares University, tehran, iran)

Received: 2020-11-25 Accepted : 2021-02-13 Published : 2022-05-01

Keywords: skew cyclic code, code over ring, Ring,

Abstract :

In thise paper we study an special type of Cyclic Codes called skewCyclic codes over the ring$R=\frac{F_p[v]}{({v}^{{2}^{k}}-1)}$ where is a prime number. This setsOf codes are the result of module (or ring) structure of the skew polynomial ring$R=[x,Q]$ where ${v}^{{2}^{k}}=1 $ and $Q$ is an Fp automorphism such that $Q(v)={v}^{{2}^{k}}-1$.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.