Commutative association schemes obtained from twin prime powers, Fermat primes, Mersenne primes

Abstract

For prime powers $q$ and $q+\epsilon$ where $\epsilon \in \{1,2\}$, an affine resolvable design from ${\mathbb{F}}_q$ and Latin squares from ${\mathbb{F}}_{q+\epsilon }$ yield a set of symmetric designs if $\epsilon =2$ and a set of symmetric group divisible designs if $\epsilon =1$. We show that these designs derive commutative association schemes, and determine their eigenmatrices.

arXiv comment17 pages