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

摘要

For prime powers $q$ and $q+arepsilon$ where $arepsilonin{1,2}$, anaffine resolvable design from $mathbb{F}_q$ and Latin squares from$mathbb{F}_{q+arepsilon}$ yield a set of symmetric designs if$arepsilon=2$ and a set of symmetric group divisible designs if$arepsilon=1$. We show that these designs derive commutative associationschemes, and determine their eigenmatrices.