# Code Constructions based on Reed-Solomon Codes

## TL;DR

This paper introduces a new code construction based on Reed-Solomon codes that allows for longer codes with lengths as factors of the field size and provides an improved decoding algorithm beyond half the minimum distance.

## Contribution

It presents a novel code construction extending Reed-Solomon codes to longer lengths and offers an analysis of an enhanced decoding algorithm.

## Key findings

- Codes with lengths as factors of the field size are achievable.
- A decoding algorithm beyond half the minimum distance is developed.
- The new construction maintains optimal properties of Reed-Solomon codes.

## Abstract

Reed--Solomon codes are a well--studied code class which fulfill the Singleton bound with equality. However, their length is limited to the size $q$ of the underlying field $\mathbb{F}_q$. In this paper we present a code construction which yields codes with lengths of factors of the field size. Furthermore a decoding algorithm beyond half the minimum distance is given and analyzed.