Commutative association schemes obtained from twin prime powers, Fermat primes, Mersenne primes
Copyright policy )Commutative association schemes obtained from twin prime powers, Fermat primes, Mersenne primes
For prime powers $q$ and $q+\varepsilon$ where $\varepsilon\in\{1,2\}$, an affine resolvable design from $\mathbb{F}_q$ and Latin squares from $\mathbb{F}_{q+\varepsilon}$ yield a set of symmetric designs if $\varepsilon=2$ and a set of symmetric group divisible designs if $\varepsilon=1$. We show that these designs derive commutative association schemes, and determine their eigenmatrices.
17 pages
symmetric group divisible design, Latin square, keywords symmetric design, Combinatorial aspects of block designs, Primes, association scheme, FOS: Mathematics, Association schemes, strongly regular graphs, Mathematics - Combinatorics, Orthogonal arrays, Latin squares, Room squares, Combinatorics (math.CO)
symmetric group divisible design, Latin square, keywords symmetric design, Combinatorial aspects of block designs, Primes, association scheme, FOS: Mathematics, Association schemes, strongly regular graphs, Mathematics - Combinatorics, Orthogonal arrays, Latin squares, Room squares, Combinatorics (math.CO)
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