# Peterson-Gorenstein-Zierler algorithm for skew RS codes

## TL;DR

This paper introduces a non-commutative decoding algorithm for skew Reed-Solomon codes, extending classical cyclic code decoding to a broader class of codes using skew polynomial rings.

## Contribution

It develops a novel non-commutative Peterson-Gorenstein-Zierler algorithm for skew RS codes, applicable to various code types over arbitrary fields.

## Key findings

- Decoding algorithm successfully applied to skew RS codes
- Extends decoding techniques beyond classical cyclic codes
- Applicable to both linear block and convolutional codes

## Abstract

We design a non-commutative version of the Peterson-Gorenstein-Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In particular, our decoding algorithm applies for block codes beyond the classical cyclic case.