Constructing few-weight linear codes and strongly regular graphs

被引：3
|
作者：
Cheng, Xiangdong [1 ]
Cao, Xiwang [1 ,2 ]
Qian, Liqin [1 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211106, Peoples R China
[2] MIIT, Key Lab Math Modelling & High Performance Comp Ai, Nanjing 211106, Peoples R China
来源：
DISCRETE MATHEMATICS | 2022年 / 345卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Linear code; Weakly regular bent function; Weight distribution; Minimal code; Strongly regular graph; 3-WEIGHT CODES; BENT FUNCTIONS; FINITE-FIELDS; 2-WEIGHT; SCHEMES;
D O I：
10.1016/j.disc.2022.113101
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Linear codes with few weights have applications in data storage systems, secret sharing schemes, graph theory and so on. In this paper, we construct a class of few-weight linear codes by choosing defining sets from cyclotomic classes and we also establish few-weight linear codes by employing weakly regular bent functions. Notably, we get some codes that are minimal and we also obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound. Finally, we get a class of strongly regular graphs with new parameters by using the obtained two-weight linear codes. (C) 2022 Elsevier B.V. All rights reserved.
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页数：12
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