The Adjacency Codes of the First Yellow Graphs

초록

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.

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