The $T_4$, and $G_4$ constructions of Costas Arrays

Abstract

We examine two particular constructions of Costas arrays known as the Taylor variant of the Lempel construction, or the $T_4$ construction, and the variant of the Golomb construction, or the $G_4$ construction. We connect these with Fibonacci primitive roots, and show that under the Extended Riemann Hypothesis, the $T_4$ and $G_4$ constructions are valid infinitely often.