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Published in: Applicable Algebra in Engineering, Communication and Computing 4/2023

27-09-2021 | Original Paper

Several classes of p-ary linear codes with few weights

Authors: Jianxin Ouyang, Hongwei Liu, Xiaoqiang Wang

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 4/2023

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Abstract

Linear codes constructed from defining sets have been extensively studied since they may have good parameters if the defining sets are chosen properly. Let \(\mathbb{F}_{p^m}\) be the finite field with \(p^m\) elements, where p is an odd prime and m is a positive integer. In this paper, we study the linear code \({\mathcal {C}}_D=\{ (\mathrm{Tr}(\alpha x))_{x \in D}\, |\, \alpha \in {\mathbb {F}}_{p^m}\}\) by choosing the defining set \(D=\{x \in {\mathbb {F}}_{p^m}^*\, | \, \mathrm{Tr}(ax^2+bx)=0\}\), where \(a\in {\mathbb {F}}_{p^m}^*\) and \(b \in {\mathbb {F}}_{p^m}\). Several classes of linear codes with explicit weight distribution are obtained. The parameters of some proposed codes are new. Several examples show that some of our codes are optimal or almost optimal according to the tables of best codes known in Grassl. Our results generalize some results in Ding and Ding (IEEE Trans. Inf. Theory 61(11):5835–5842, 2015), Li et al. (Disc. Math. 241:25–38, 2018).

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Metadata
Title
Several classes of p-ary linear codes with few weights
Authors
Jianxin Ouyang
Hongwei Liu
Xiaoqiang Wang
Publication date
27-09-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 4/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00527-2

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