A link between combinatorial designs and three-weight linear codes
type: Item
instance of: scholarly article
title: A link between combinatorial designs and three-weight linear codes
zbMATH Open document ID: 1388.05024
author: Oktay Olmez
published in: Designs, Codes and Cryptography
publication date: 2018-04-10T00:00:00Z
review text: Links between different discrete structures (linear codes, combinatorial designs, connected graphs, some cryptographic primitives, etc.) have been a subject of research of many authors. By these links some obtained results about a given structure can be applied into the others. In this paper, the author describes that partial geometric designs can be constructed from 3-weight codes, almost bent functions and ternary weakly regular bent functions. They show that existence of certain partial geometric designs is equivalent to existence of some families of 3-weight codes. Also, the author introduces a family of graphs related to a family of 3-weight codes. Finally, he provide a classification of Cayley graphs obtained from partial geometric difference sets and weakly regular bent functions.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 06E30
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 6858025
zbMATH Keywords: partial geometric designs
zbMATH Keywords: partial geometric difference sets
zbMATH Keywords: weakly regular bent functions
zbMATH Keywords: almost bent functions
zbMATH Keywords: plateaued functions
zbMATH Keywords: three-weight linear codes
zbMATH Keywords: strongly regular graphs
reviewed by: Zlatko Varbanov
MaRDI profile type: Publication
full work available at URL: s10623-017-0363-3
OpenAlex ID: W2610217826
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DOI: 10.1007/S10623-017-0363-3
description: scientific article; zbMATH DE number 6858025