Butson Hadamard Matrices from Pairs of Gauss Sums

Cheng Yiin Ong, Bernhard Schmidt

Let $q$ be a prime power. We give a construction of Butson Hadamard matrices $BH((F_q\times F_q,+),lcm(6,d))$ for any divisor $d>1$ of $q-1$. Most character values of the group rin…