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

Theory of Approximation and Applications

مقاله 4، دوره 16، شماره 1، مرداد 2022، صفحه 21-32   

نوع مقاله: Research Articles

نویسنده

Alireza Soleimani^*

Faculty of Mathematics, Tarbiat Modares University, tehran, iran

چکیده

In thise paper we study an special type of Cyclic Codes called skew
Cyclic codes over the ring$R=\frac{F_p[v]}{({v}^{{2}^{k}}-1)}$ where is a prime number. This sets
Of 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 code
Look like a module and proof some properties.

کلیدواژه‌ها

Skew cyclic code؛ Ring؛ Code over ring