The Euclidean Algorithm for Generalized Minimum Distance Decoding of Reed-Solomon Codes

TL;DR

This paper introduces a novel decoding algorithm for Reed-Solomon codes that integrates Generalized Minimum Distance decoding with the extended Euclidean algorithm, achieving quadratic complexity.

Contribution

It presents a new method that combines GMD decoding with the Euclidean algorithm, simplifying the decoding process for Reed-Solomon codes.

Findings

Complexity of O(n^2) for the proposed algorithm

Decoding process similar to Euclidean algorithm steps

Effective for generalized minimum distance decoding

Abstract

This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps taken to perform the Generalized Minimum Distance decoding are similar to those performed by the extended Euclidean algorithm. The resulting algorithm has a complexity of O(n^2).