New open problems related to old conjectures by Helleseth
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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.
KeywordsFinite fields Weil sums Exponential sums Cross-correlation M-sequence
The first author was supported in part by a Research, Scholarship, and Creative Activity Award from California State University, Northridge. The first author was also supported in part by the Institut de Mathématiques de Toulon at Université de Toulon as a visiting professor. The authors thank anonymous reviewers for helpful corrections and suggestions.
- 1.Aubry, Y., Katz, D.J., Langevin, P.: Cyclotomy of Weil sums of binomials (2013) arXiv:1312.3889 [math.NT]
- 2.Aubry, Y., Langevin, P.: On a conjecture of Helleseth. In: Algebraic informatics, volume 8080 of Lecture Notes in Comput. Sci., pp 113–118. Springer, Heidelberg (2013)Google Scholar
- 3.Blokhuis, A., Calderbank, A.R.: Unpublished noteGoogle Scholar
- 9.Katz, D.J.: Divisibility of Weil sums of binomials (2014) arXiv:1407.7923 [math.NT]
- 13.Langevin, P.: Numerical projects page: spectra of power maps (2007). http://langevin.univ-tln.fr/project/spectrum
- 14.Langevin, P.: Numerical projects page : nice exponents, 2013 and 2015. http://langevin.univ-tln.fr/project/expo