Characterization of the skew cyclic codes over Fp+vFp

TL;DR

This paper characterizes skew cyclic codes over the ring Fp+vFp, providing explicit descriptions, properties, and construction methods, including encoding and decoding processes, especially when certain divisibility conditions are met.

Contribution

It offers a comprehensive characterization of skew cyclic codes over Fp+vFp, including explicit code descriptions and construction techniques under specific algebraic conditions.

Findings

Explicit characterization of skew cyclic codes over Fp+vFp

Construction methods for codes with specific length conditions

Examples illustrating encoding and decoding processes

Abstract

We study cyclic codes with arbitrary length over Fp+vFp where theta(v)=av, a in Fp and v^2=0. We characterize all existing codes in case of O(theta)|n by using certain projections from (Fp+vFp)[x;theta] to Fp[x]. We provide an explicit expression for the ensemble of all possible codes. We also prove useful properties of these codes in the case where O(theta)|n does not hold. We provide results and examples to illustrate how the codes are constructed and how their encoding and decoding are realized.