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Commutative association schemes obtained from twin prime powers, Fermat primes, Mersenne primes. (English) Zbl 1433.05334
Summary: 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.

MSC:
05E30 Association schemes, strongly regular graphs
05B05 Combinatorial aspects of block designs
05B15 Orthogonal arrays, Latin squares, Room squares
11A41 Primes
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