New Open Problems Related to Old Conjectures by Helleseth
Daniel J. Katz, Philippe Langevin
TL;DR
This paper surveys recent advances in the Fourier spectra of power permutations over finite fields and introduces new open problems related to longstanding conjectures by Helleseth from the 1970s.
Contribution
It consolidates recent research developments and formulates new open problems concerning classical conjectures in finite field theory.
Findings
Recent results on Fourier spectra of power permutations
Identification of gaps in current understanding
Proposals for future research directions
Abstract
Recently, very interesting results have been obtained concerning the Fourier spectra of power permutations over a finite field. In this note we survey the recent ideas of Aubry, Feng, Katz, and Langevin, and we pose new open problems related to old conjectures proposed by Helleseth in the middle of the seventies.
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Taxonomy
TopicsCoding theory and cryptography · Limits and Structures in Graph Theory · Analytic Number Theory Research