Algebraic symmetries of generic (m+1)(m+1) dimensional periodic Costas arrays

In this work we present two generators for the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\mathbb{Z}_p)^m$ groups: one that is defined by multiplication on $m$ dimensions and the other by shear (addition) on $m$ dimensions. Through exhaustive search we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\mathbb{Z}_p)^m$ groups