Three experimental pearls in Costas arrays
Konstantinos Drakakis
TL;DR
This paper presents three experimental findings related to Costas arrays, exploring unexplained phenomena in their structure and correlation properties, with potential implications for applications in signal processing.
Contribution
It reports novel experimental results on Costas arrays, focusing on diagonal dot counts, parity distributions, and cross-correlation in specific finite fields, where theoretical explanations are still lacking.
Findings
Number of dots on main diagonal of exponential Welch arrays analyzed
Parity populations of Golomb arrays in characteristic 2 fields studied
Maximal cross-correlation between Welch and Golomb arrays in Sophie Germain prime fields examined
Abstract
The results of 3 experiments in Costas arrays are presented, for which theoretical explanation is still not available: the number of dots on the main diagonal of exponential Welch arrays, the parity populations of Golomb arrays generated in fields of characteristic 2, and the maximal cross-correlation between pairs of Welch or Golomb arrays generated in fields of size equal to a Sophie Germain prime.
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Taxonomy
TopicsStructural Analysis and Optimization