# On Fractional Decoding of Reed-Solomon Codes

## TL;DR

This paper introduces a probabilistic fractional decoding algorithm for Reed-Solomon codes that extends decoding capabilities beyond traditional limits, with theoretical failure bounds and illustrative examples.

## Contribution

It proposes a novel probabilistic fractional decoding method for Reed-Solomon codes and provides an upper bound on its failure probability.

## Key findings

- Decoding performance exceeds traditional limits
- Failure probability is theoretically bounded
- Algorithm effectiveness demonstrated through examples

## Abstract

We define a virtual projection of a Reed-Solomon code $RS(q^{l},n,k)$ to an $RS(q,n,k)$ Reed-Solomon code. A new probabilistic decoding algorithm that can be used to perform fractional decoding beyond the $\alpha$- decoding radius is considered. An upper bound for the failure probability of the new algorithm is given, and the performance is illustrated by examples.