Infinite families of 2-designs from linear codes

被引：10
作者：
Du, Xiaoni [1 ,2 ]
Wang, Rong [1 ]
Tang, Chunming [3 ]
Wang, Qi [4 ]
机构：
[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China
[2] Guilin Univ Elect Technol, Guangxi Key Lab Cryptog & Informat Secur, Guilin 541004, Guangxi, Peoples R China
[3] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Sichuan, Peoples R China
[4] Southern Univ Sci & Technol, Dept Comp Sci & Engn, Shenzhen 518055, Guangdong, Peoples R China
来源：
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2022年 / 33卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Affine-invariant code; Cyclic code; Exponential sum; Linear code; Weight distribution; 2-design; GAUSS SUMS; 3-DESIGNS;
D O I：
10.1007/s00200-020-00438-8
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
Interplay between coding theory and combinatorialt-designs has attracted a lot of attention. It is well known that the supports of all codewords of a fixed Hamming weight in a linear code may hold at-design. In this paper, we first settle the weight distributions of two classes of linear codes, and then determine the parameters of infinite families of 2-designs held in these codes.
引用
收藏
页码：193 / 211
页数：19
相关论文
共 25 条
[21]  
Reid C, 2010, ELECTRON J COMB, V#DS18, P1
[22]  
Tonchev V.D., 2007, HDB COMBINATORIAL DE, P677, DOI DOI 10.1016/S1570-7954(07)05005-X
[23]  
Tonchev VD, 1998, HANDBOOK OF CODING THEORY, VOLS I & II, P1229
[24]   Hasse-Davenport curves, Gauss sums, and weight distributions of irreducible cyclic codes [J].
vanderVlugt, M .
JOURNAL OF NUMBER THEORY, 1995, 55 (02) :145-159
[25]   Combinatorial t-designs from quadratic functions [J].
Xiang, Can ;
Ling, Xin ;
Wang, Qi .
DESIGNS CODES AND CRYPTOGRAPHY, 2020, 88 (03) :553-565
123