Divisible difference families from Galois rings $$GR(4,n)$$ GR ( 4 , n ) and Hadamard matrices

Abstract

We give a new construction of difference families generalizing Szekeres's difference families Szekeres (Enseignment Math 15:269---278, 1969). As an immediate consequence, we obtain some new examples of difference families with several blocks in multiplicative subgroups of finite fields. We also prove that there exists an infinite family of divisible difference families with two blocks in a unit subgroup of the Galois ring $$GR(4,n)$$ GR ( 4 , n ) . Furthermore, we obtain a new construction method of symmetric Hadamard matrices by using divisible difference families and a new array.