Unique Decoding of Hyperderivative Reed-Solomon Codes

TL;DR

This paper introduces a novel decoding algorithm for Hyperderivative Reed-Solomon codes under the NRT metric, enhancing error correction capabilities in noisy communication channels.

Contribution

It presents a Welch-Berlekamp algorithm specifically designed for the unique decoding of NRT Hyperderivative Reed-Solomon codes, a new approach in coding theory.

Findings

Successful decoding of HRS codes with the proposed algorithm

Improved error correction performance under the NRT metric

Extension of classical decoding techniques to hyperderivative codes

Abstract

Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental problem in coding theory and practice is to efficiently decode the received word with errors to obtain the transmitted codeword. In this paper, we consider the decoding problem of Hyperderivative Reed-Solomon (HRS) codes with respect to the NRT metric. Specifically, we propose a Welch-Berlekamp algorithm for the unique decoding of NRT HRS codes.