The Adjacency Codes of the First Yellow Graphs

被引：0

作者：

Shi, Minjia ^{[1
,2
]}

Li, Shitao ^{[3
]}

Kim, Jon-Lark ^{[4
]}

Sole, Patrick ^{[5
]}

机构：

[1] Anhui Univ, Sch Math Sci, Minist Educ, Key Lab Intelligent Comp & Signal Proc, Hefei 230601, Peoples R China

[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China

[3] Anhui Univ, Sch Math Sci, Hefei 230026, Peoples R China

[4] Sogang Univ, Dept Math, Seoul, South Korea

[5] Aix Marseille Univ, CNRS, Cent Marseille, I2M, Marseille, France

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2023年 / 36卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Cyclic codes; strongly regular graphs; adjacency codes; self-orthogonal codes;

D O I：

10.1007/s11424-023-1518-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The authors study the binary codes spanned by the adjacency matrices of the strongly regular graphs (SRGs) on at most two hundred vertices whose existence is unknown. The authors show that in length less than one hundred they cannot be cyclic, except for the exceptions of the SRGs of parameters (85, 42, 20, 21) and (96, 60, 38, 36). In particular, the adjacency code of a (85,42, 20, 21) is the zero-sum code. In the range [100, 200] the authors find 29 SRGs that could possibly have a cyclic adjacency code.

引用

页码：1757 / 1768

页数：12

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