The T_4 and G_4 constructions of Costas arrays

摘要

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.