The $T_{4}$ and $G_{4}$ constructions of Costas arrays

Tim Trudgian; Qiang Wang

The $T_{4}$ and $G_{4}$ constructions of Costas arrays

Number Theory 2014-09-25 v1 Combinatorics

Authors: Tim Trudgian , Qiang Wang

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 constructions with the concept of Fibonacci primitive roots, and show that under the Extended Riemann Hypothesis the $T_{4}$ and $G_{4}$ constructions are valid infinitely often.

Keywords

Costas arrays $T_{4}$ construction $G_{4}$ construction Fibonacci primitive roots Extended Riemann Hypothesis Lempel construction Golomb construction

Cite

@article{arxiv.1409.6827,
  title  = {The $T_{4}$ and $G_{4}$ constructions of Costas arrays},
  author = {Tim Trudgian and Qiang Wang},
  journal= {arXiv preprint arXiv:1409.6827},
  year   = {2014}
}

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5 pages

The $T_{4}$ and $G_{4}$ constructions of Costas arrays

Abstract

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