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

We give a new construction of difference families generalizing Szekeres’s difference families [17]. 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). Furthermore, we obtain a new construction method of symmetric Hadamard matrices by using divisible difference families and a new array.