Linear Codes from Two Weakly Regular Plateaued Balanced Functions

Linear codes with a few weights have been extensively studied due to their wide applications in secret sharing schemes, strongly regular graphs, association schemes, and authentication codes. In this paper, we choose the defining sets from two distinct weakly regular plateaued balanced functions, ba...

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Detalles Bibliográficos
Autores principales: Yang, Shudi, Zhang, Tonghui, Li, Ping
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955120/
https://www.ncbi.nlm.nih.gov/pubmed/36832735
http://dx.doi.org/10.3390/e25020369
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author Yang, Shudi
Zhang, Tonghui
Li, Ping
author_facet Yang, Shudi
Zhang, Tonghui
Li, Ping
author_sort Yang, Shudi
collection PubMed
description Linear codes with a few weights have been extensively studied due to their wide applications in secret sharing schemes, strongly regular graphs, association schemes, and authentication codes. In this paper, we choose the defining sets from two distinct weakly regular plateaued balanced functions, based on a generic construction of linear codes. Then we construct a family of linear codes with at most five nonzero weights. Their minimality is also examined and the result shows that our codes are helpful in secret sharing schemes.
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spelling pubmed-99551202023-02-25 Linear Codes from Two Weakly Regular Plateaued Balanced Functions Yang, Shudi Zhang, Tonghui Li, Ping Entropy (Basel) Article Linear codes with a few weights have been extensively studied due to their wide applications in secret sharing schemes, strongly regular graphs, association schemes, and authentication codes. In this paper, we choose the defining sets from two distinct weakly regular plateaued balanced functions, based on a generic construction of linear codes. Then we construct a family of linear codes with at most five nonzero weights. Their minimality is also examined and the result shows that our codes are helpful in secret sharing schemes. MDPI 2023-02-17 /pmc/articles/PMC9955120/ /pubmed/36832735 http://dx.doi.org/10.3390/e25020369 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Yang, Shudi
Zhang, Tonghui
Li, Ping
Linear Codes from Two Weakly Regular Plateaued Balanced Functions
title Linear Codes from Two Weakly Regular Plateaued Balanced Functions
title_full Linear Codes from Two Weakly Regular Plateaued Balanced Functions
title_fullStr Linear Codes from Two Weakly Regular Plateaued Balanced Functions
title_full_unstemmed Linear Codes from Two Weakly Regular Plateaued Balanced Functions
title_short Linear Codes from Two Weakly Regular Plateaued Balanced Functions
title_sort linear codes from two weakly regular plateaued balanced functions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955120/
https://www.ncbi.nlm.nih.gov/pubmed/36832735
http://dx.doi.org/10.3390/e25020369
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AT zhangtonghui linearcodesfromtwoweaklyregularplateauedbalancedfunctions
AT liping linearcodesfromtwoweaklyregularplateauedbalancedfunctions

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