The Adjacency Codes of the First Yellow Graphs

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,...

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Bibliographic Details
Published inJournal of systems science and complexity Vol. 36; no. 4; pp. 1757 - 1768
Main Authors Shi, Minjia, Li, Shitao, Kim, Jon-Lark, Solé, Patrick
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023
Springer Nature B.V
Subjects
Apexes
Binary codes
Complex Systems
Control
Graphs
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Statistics
Systems Theory
strongly regular graphs
self-orthogonal codes
Cyclic codes
adjacency codes
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Summary: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.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-023-1518-0