A Fast Generalized Minimum Distance Decoder for Reed-Solomon Codes Based on the Extended Euclidean Algorithm

TL;DR

This paper introduces a rapid decoding method for Reed-Solomon codes using the extended Euclidean algorithm, enabling efficient generalized minimum distance decoding with reduced computational complexity.

Contribution

It proposes a novel approach to basis polynomial determination that improves decoding efficiency for Reed-Solomon codes.

Findings

Decoding complexity is reduced to O(nd).

The method effectively determines basis polynomials for decoding.

It enhances the speed of generalized minimum distance decoding.

Abstract

This paper presents a method to determine a set of basis polynomials from the extended Euclidean algorithm that allows Generalized Minimum Distance decoding of Reed-Solomon codes with a complexity of O(nd).