# A Decoding Approach to Reed-Solomon Codes from Their Definition

## TL;DR

This paper presents a new, more intuitive decoding approach for Reed-Solomon codes, making error correction concepts more accessible for beginners by deriving the algorithm from fundamental definitions.

## Contribution

A self-contained decoding method for Reed-Solomon codes based on polynomial interpolation degree, simplifying understanding for nonexperts.

## Key findings

- Decoding algorithm derived from interpolation polynomial degree
- Algorithm is more natural and easier to understand than classical methods
- Related to Peterson-Gorenstein-Zierler algorithm

## Abstract

Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple and it is difficult to fit them in introductory courses for undergraduates. We introduce a new decoding approach, in a self-contained presentation, which we think may be appropriate for introducing error correction of Reed-Solomon codes to nonexperts. In particular, we interpret Reed-Solomon codes by means of the degree of the interpolation polynomial of the code words and from this derive a decoding algorithm. Compared to the classical algorithms, our algorithm appears to arise more naturally from definitions and to be easier to understand. It is related to the Peterson-Gorenstein-Zierler algorithm.