Speaker: Liu Huaning, professor and doctoral supervisor, Northwest University

Date: November 26, 2024

Time: 10:00-11:00 am

Location: B1044, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

In the most interesting case of safe prime powers $q$, Gomez and Winterhof showed that a subfamily of the family of Golomb Costas permutations of $\{1,2,\Idots, q-2\}$ of size $\varphi(q-1)$ has maximal cross-correlation of order of magnitude at most $q^{1/2}$. In this talk 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 Szemeredi-Trotter theorem for finite fields. This is a joint work with Arne Winterhof.

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https://www.view.sdu.edu.cn/info/1020/197303.htm