On constructions of bent, semi-bent and five valued spectrum functions from old bent functions

Sihem Mesnager; Fengrong Zhang

doi:10.3934/amc.2017026

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2017, Volume 11, Issue 2: 339-345. Doi: 10.3934/amc.2017026

This issue Previous Article On the covering radius of some binary cyclic codes Next Article On construction of bent functions involving symmetric functions and their duals

On constructions of bent, semi-bent and five valued spectrum functions from old bent functions

Sihem Mesnager^1, and
Fengrong Zhang^2,3, ,

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.
Department of Mathematics, University of Paris Ⅷ and Paris ⅩⅢ, LAGA, UMR 7539, CNRS, Sorbonne Paris Cité

^* Corresponding author
^* Corresponding author

Received: February 2016

Revised: March 2016

Published: September 2017

This work was supported by National Science Foundation of China (Grant No. 61303263), and in part by the Fundamental Research Funds for the Central Universities (Grant No. 2015XKMS086), and in part by the China Postdoctoral Science Foundation funded project (Grant No. 2015T80600)

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Abstract

The paper presents methods for designing functions having many applications in particular to construct linear codes with few weights. The former codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. We firstly provide new secondary constructions of bent functions generalizing the well-known Rothaus' constructions as well as their dual functions. From our generalization, we show that we are able to compute the dual function of a bent function built from Rothaus' construction. Next we present a result leading to a new method for constructing semi-bent functions and few Walsh transform values functions built from bent functions.

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Mathematics Subject Classification: 06E30, 94A60.

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References

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