Construction of Self-dual Codes over $F_p+vF_p$

TL;DR

This paper characterizes all self-dual codes over the ring $F_p+vF_p$ with $v^2=v$, based on self-dual codes over the finite field $F_p$, and provides explicit construction methods.

Contribution

It introduces a complete classification and explicit construction of self-dual codes over the ring $F_p+vF_p$, extending known results from finite fields.

Findings

All self-dual codes over $F_p+vF_p$ are characterized in terms of codes over $F_p$.

Explicit construction methods for these codes are provided.

The results generalize the theory of self-dual codes to a new algebraic setting.

Abstract

In this paper, we determine all self-dual codes over $F_p+vF_p$ ($v^2=v$) in terms of self-dual codes over the finite field $F_p$ and give an explicit construction for self-dual codes over $F_p+vF_p$, where $p$ is a prime.