New hemisystems of the Hermitian surface

Abstract

Finding Hemisystems is a challenging problem and just few examples arising from the Hermitian surface are known. A recent method to obtain Hemisystems is based on using maximal curves. Along this side of research, we provide new examples of Hemisystems in $PG(3,p^2)$, for each prime of the form $p=1+4a^2$, with $a$ integer. Last, we use these results to obtain two weight linear codes and strongly regular graphs.

arXiv admin note: text overlap with arXiv:1710.06335 by other authors