Isomorphism classes of association schemes induced by Hadamard matrices

2014/07/28 by Hirasaka, Mitsugu, Kim, Kijung, Yu, Hyonju
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.7346

Abstract

Every Hadamard matrix H of order n > 1 induces a graph with 4n vertices, called the Hadamard graph Γ(H) of H. Since Γ(H) is a distance-regular graph with diameter 4, it induces a 4-class association scheme (Ω, S) of order 4n. In this article we deal with fission schemes of (Ω, S) under certain conditions, and for such a fission scheme we estimate the number of isomorphism classes with the same intersection numbers as the fission scheme.

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