Generalized Reed-Solomon codes over number fields and exact gradient coding

Irwansyah; Intan Muchtadi-Alamsyah; Fajar Yuliawan; Muhammad Irfan Hidayat

doi:10.3934/math.2024464

AIMS Mathematics (Mar 2024)

Generalized Reed-Solomon codes over number fields and exact gradient coding

Irwansyah,
Intan Muchtadi-Alamsyah,
Fajar Yuliawan ,
Muhammad Irfan Hidayat

Affiliations

Irwansyah: 1. Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Indonesia
Intan Muchtadi-Alamsyah: 2. Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Fajar Yuliawan: 2. Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Muhammad Irfan Hidayat: 2. Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia

DOI: https://doi.org/10.3934/math.2024464
Journal volume & issue: Vol. 9, no. 4
pp. 9508 – 9518

Abstract

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This paper describes generalized Reed-Solomon (GRS) codes over number fields that are invariant under certain permutations. We call these codes generalized quasi-cyclic (GQC) GRS codes. Moreover, we describe an application of GQC GRS codes over number fields to exact gradient coding.

Published in AIMS Mathematics

ISSN: 2473-6988 (Online)
Publisher: AIMS Press
Country of publisher: United States
LCC subjects: Science: Mathematics
Website: http://www.aimspress.com/journal/Math

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