101 research outputs found
Symmetric Bush-type generalized Hadamard matrices and association schemes
We define Bush-type generalized Hadamard matrices over abelian groups and
construct symmetric Bush-type generalized Hadamard matrices over the additive
group of finite field , a prime power. We then show and study
an association scheme obtained from such generalized Hadamard matrices.Comment: 10 page
Implementing Brouwer's database of strongly regular graphs
Andries Brouwer maintains a public database of existence results for strongly
regular graphs on vertices. We implemented most of the infinite
families of graphs listed there in the open-source software Sagemath, as well
as provided constructions of the "sporadic" cases, to obtain a graph for each
set of parameters with known examples. Besides providing a convenient way to
verify these existence results from the actual graphs, it also extends the
database to higher values of .Comment: 18 pages, LaTe
Hadamard matrices related to the projective planes
Let be the order of a (quaternary) Hadamard matrix. It is shown that the
existence of a projective plane of order is equivalent to the existence of
a balancedly multi-splittable (quaternary) Hadamard matrix of order .Comment: 9 page
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