Abstract
In this note, we analyze power permutations having a three valued spectrum. We give new results and new proofs of results previously obtained by coding theory. We apply them to prove that Hellesth’s conjecture is true for dimension 32.
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References
Calderbank, A.R., Blokhuis, A.: (unpublished)
Calderbank, A.R., McGuire, G., Poonen, B., Rubinstein, M.: On a conjecture of Helleseth regarding pairs of binary m-sequences. IEEE Trans. Inform. Theory 42(3), 988–990 (1996)
Helleseth, T.: Some results about the cross-correlation function between two maximal linear sequences. Discrete Math. 16(3), 209–232 (1976)
Katz, N., Livné, R.: Sommes de Kloosterman et courbes elliptiques universelles en caractéristiques 2 et 3. C. R. Acad. Sci. Paris Sér. I. Math. 309(11), 723–726 (1989)
Langevin, P.: Numerical projects page (2007), http://langevin.univ-tln.fr/project/spectrum
Langevin, P., Véron, P.: Non-linearity of power functions. Designs Codes and Cryptography 37(1) (2005)
McGuire, G.M., Calderbank, A.R.: Proof of a conjecture of Sarwate and Pursley regarding pairs of binary m-sequences. IEEE Trans. Inform. Theory 41(4), 1153–1155 (1995)
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ÇakÇak, E., Langevin, P. (2010). Power Permutations in Dimension 32. In: Carlet, C., Pott, A. (eds) Sequences and Their Applications – SETA 2010. SETA 2010. Lecture Notes in Computer Science, vol 6338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15874-2_14
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DOI: https://doi.org/10.1007/978-3-642-15874-2_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15873-5
Online ISBN: 978-3-642-15874-2
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