A Construction of Layered Relative Difference Sets Using Galois Rings

Abstract

Using a similar framework to $[7]$, we construct a family of relative difference sets in $P\times (Z_{p^{2}r}^{2}t)$, where $P$ is the forbidden subgroup. We only require that $P$ be an abelian group of order $p^t$. The construction makes use of character theory and the structure of the Galois ring $GR(p^{2r},t)$, and in particular the Teichmüller set for the Galois ring.