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

Abstract

For prime powers q and q+ε where ε∈{1,2}, an affine resolvable design from Fq and Latin squares from Fq+ε yield a set of symmetric designs if ε=2 and a set of symmetric group divisible designs if ε=1. We show that these designs derive commutative association schemes, and determine their eigenmatrices.