On solving isomorphism problems about 2-designs using block intersection numbers
Christian Kaspers, Alexander Pott · Finite Fields and Their Applications · 2020
In this paper, we give a partial solution to a new isomorphism problem about 2-(v, k, k − 1) designs from disjoint difference families in finite fields and Galois rings. Our results are obtained by carefully calculating and bounding some block intersection numbers, and we give insight on the limitations of this technique. Moreover, we present results on cyclotomic numbers, the multiplicities of block intersection numbers of certain designs and on the structure of Galois rings of characteristic p2.