Cryptography and Communications

, Volume 8, Issue 2, pp 175–189 | Cite as

New open problems related to old conjectures by Helleseth



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.


Finite 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.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.California State UniversityNorthridgeUSA
  2. 2.Université de ToulonLa GardeFrance

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