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Using double Weil sums in finding the c-boomerang connectivity table for monomial functions on finite fields

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In this paper we characterize the c-Boomerang Connectivity Table (BCT), \(c\ne 0\) (thus, including the classical \(c=1\) case), for all monomial function \(x^d\) in terms of characters and Weil sums on the finite field \({\mathbb F}_{p^n}\), for an odd prime p. We further simplify these expressions for the Gold functions \(x^{p^k+1}\) for all \(1\le k<n\), and p odd. It is the first such attempt for a complete description for the classical BCT and its relative c-BCT, for all parameters involved, albeit in terms of characters.

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Acknowledgements

The author would like to thank the editor for the prompt handling of our paper, as well as the referees for their useful comments, which improved our paper.

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  1. Applied Mathematics Department, Naval Postgraduate School, Monterey, CA, 93943, USA

    Pantelimon Stănică

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Stănică, P. Using double Weil sums in finding the c-boomerang connectivity table for monomial functions on finite fields. AAECC 34, 581–602 (2023). https://doi.org/10.1007/s00200-021-00520-9

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