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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:
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
Descripción
Sumario: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.