Improved Decoding Algorithms for MDS and Almost-MDS Codes From Twisted GRS Codes

IF 2.9 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2025-07-30 DOI:10.1109/TIT.2025.3594174

Guodong Wang;Hongwei Liu;Jinquan Luo

引用次数: 0

Abstract

In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further study decoding of almost-MDS TGRS codes and provide a decoding algorithm. These two decoding algorithms are more efficient in terms of performance compared with the decoding algorithms presented in [Sun et al., IEEE-TIT, 2024] and [Sui et al., IEEE-TIT, 2023] respectively. Moreover, these two optimized decoding algorithms can be applied to the decoding of a more general class of twisted Goppa codes.

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基于扭曲GRS码的MDS和近MDS码译码改进算法

本文首先研究了一类扭曲广义Reed-Solomon （TGRS）码的译码，给出了TGRS码的关键方程的精确刻画，并提出了译码算法。其次，进一步研究了近mds TGRS码的译码，并给出了译码算法。与[Sun et al., IEEE-TIT， 2024]和[Sui et al., IEEE-TIT， 2023]中提出的解码算法相比，这两种解码算法在性能上更加高效。此外，这两种优化的解码算法可以应用于更一般的扭曲Goppa码的解码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.