# American Institute of Mathematical Sciences

May 2017, 11(2): 347-352. doi: 10.3934/amc.2017027

## On construction of bent functions involving symmetric functions and their duals

 1 Department of Mathematics, University of Paris Ⅷ and Paris ⅩⅢ and Télécom ParisTech, LAGA, UMR 7539, CNRS, Sorbonne Paris Cité 2 School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China 3 State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China

* Corresponding author

Received  February 2016 Revised  March 2016 Published  May 2017

In this paper, we firstly compute the dual functions of elementary symmetric bent functions. Next, we derive a new secondary construction of bent functions (given with their dual functions) involving symmetric bent functions, leading to a generalization of the well-know Rothaus' construction.

Citation: Sihem Mesnager, Fengrong Zhang, Yong Zhou. On construction of bent functions involving symmetric functions and their duals. Advances in Mathematics of Communications, 2017, 11 (2) : 347-352. doi: 10.3934/amc.2017027
##### References:
 [1] C. Carlet, Boolean functions for cryptography and error correcting codes, in Boolean Models and Methods in Mathematics, Computer Science, and Engineering (eds. Y. Crama and P. Hammer), Cambridge Univ. Press, 2010,257-397. doi: 10.1017/CBO9780511780448. [2] C. Carlet and S. Mesnager, Four decades of research on bent functions, Des. Codes Crypt., 78 (2016), 5-50. doi: 10.1007/s10623-015-0145-8. [3] S. Mesnager, Bent Functions: Fundamentals and Results, Springer-Verlag, 2016. doi: 10.1007/978-3-319-32595-8. [4] O. S. Rothaus, On "bent" functions, J. Combin. Theory Ser. A, 20 (1976), 300-305. [5] S. Mesnager and F. Zhang, On constructions of bent, semi-bent and five valued spectrum functions from old bent functions, Adv. Math. Commun., 11 (2017), 339-345.

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##### References:
 [1] C. Carlet, Boolean functions for cryptography and error correcting codes, in Boolean Models and Methods in Mathematics, Computer Science, and Engineering (eds. Y. Crama and P. Hammer), Cambridge Univ. Press, 2010,257-397. doi: 10.1017/CBO9780511780448. [2] C. Carlet and S. Mesnager, Four decades of research on bent functions, Des. Codes Crypt., 78 (2016), 5-50. doi: 10.1007/s10623-015-0145-8. [3] S. Mesnager, Bent Functions: Fundamentals and Results, Springer-Verlag, 2016. doi: 10.1007/978-3-319-32595-8. [4] O. S. Rothaus, On "bent" functions, J. Combin. Theory Ser. A, 20 (1976), 300-305. [5] S. Mesnager and F. Zhang, On constructions of bent, semi-bent and five valued spectrum functions from old bent functions, Adv. Math. Commun., 11 (2017), 339-345.
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