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arXiv · 2408.14330

On the cross-correlation of Golomb Costas permutations

Huaning Liu·Arne Winterhof
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Abstract

In the most interesting case of safe prime powers $q$, Gómez and Winterhof showed that a subfamily of the family of Golomb Costas permutations of $\{1,2,\ldots,q-2\}$ of size $φ(q-1)$ has maximal cross-correlation of order of magnitude at most $q^{1/2}$. In this paper we study a larger family of Golomb Costas permutations and prove a weaker bound on its maximal cross-correlation. Considering the whole family of Golomb Costas permutations we show that large cross-correlations are very rare. Finally, we collect several conditions for a small cross-correlation of two Costas permutations. Our main tools are the Weil bound and the Szemerédi-Trotter theorem for finite fields.

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Huaning Liu, Arne Winterhof. 2024-08-26. On the cross-correlation of Golomb Costas permutations. https://arxiv.org/abs/2408.14330

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