Special bent and near-bent functions

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February 2014, 8(1): 21-33. doi: 10.3934/amc.2014.8.21

Special bent and near-bent functions

1.	IMATH(IAA), Université du Sud Toulon-Var, 83957 La Garde Cedex, France

Received December 2011 Revised November 2013 Published January 2014

Abstract
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Starting from special near-bent functions in dimension $2t-1$ we construct bent functions in dimension $2t$ having a specific derivative. We deduce new families of bent functions.

Keywords: near-bent functions., Bent functions.

Mathematics Subject Classification: 11T71, 94B0.

Citation: Jacques Wolfmann. Special bent and near-bent functions. Advances in Mathematics of Communications, 2014, 8 (1) : 21-33. doi: 10.3934/amc.2014.8.21

References:

[1]	A. Canteault, C. Carlet, P. Charpin and C. Fontaine, On cryptographic properties of the cosets of R(1,m),, IEEE Trans. Inform. Theory, 47 (2001), 1494. doi: 10.1109/18.923730. Google Scholar
[2]	A. Canteault and P. Charpin, Decomposing bent functions,, IEEE Trans. Inform. Theory, 49 (2003), 2004. doi: 10.1109/TIT.2003.814476. Google Scholar
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show all references

References:

[1]	A. Canteault, C. Carlet, P. Charpin and C. Fontaine, On cryptographic properties of the cosets of R(1,m),, IEEE Trans. Inform. Theory, 47 (2001), 1494. doi: 10.1109/18.923730. Google Scholar
[2]	A. Canteault and P. Charpin, Decomposing bent functions,, IEEE Trans. Inform. Theory, 49 (2003), 2004. doi: 10.1109/TIT.2003.814476. Google Scholar
[3]	J. F. Dillon, Elementary Hadamard Difference Sets,, Ph.D thesis, (1974). Google Scholar
[4]	J. F. Dillon, Multiplicative difference sets via additive characters,, Des. Codes Cryptogr., 17 (1999), 225. doi: 10.1023/A:1026435428030. Google Scholar
[5]	R. Gold, Maximal recursive squences with 3-valued recursive cross-correlation functions,, IEEE Trans. Inform. Theory, 14 (1968), 154. doi: 10.1109/TIT.1968.1054106. Google Scholar
[6]	X. D. Hou, Cubic bent functions,, Discrete Math., 189 (1998), 149. doi: 10.1016/S0012-365X(98)00008-9. Google Scholar
[7]	G. Leander and G. McGuire, Construction of bent functions from near-bent functions,, J. Combin. Theory Ser. A, 116 (2009), 960. doi: 10.1016/j.jcta.2008.12.004. Google Scholar
[8]	O. S. Rothaus, On bent functions,, J. Combin. Theory Ser. A, 20 (1976), 300. doi: 10.1016/0097-3165(76)90024-8. Google Scholar
[9]	J. Wolfmann, Bent functions and coding theory,, in Difference Sets, (1999), 393. Google Scholar
[10]	J. Wolfmann, Cyclic code aspects of bent functions,, in Finite Fields Theory and Applications, (2010), 363. doi: 10.1090/conm/518/10218. Google Scholar

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