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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.

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