Explicit constructions of bent functions from pseudo-planar functions

Kanat Abdukhalikov; Sihem Mesnager

doi:10.3934/amc.2017021

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2017, Volume 11, Issue 2: 293-299. Doi: 10.3934/amc.2017021

This issue Previous Article Certain sextics with many rational points Next Article Explicit formulas for monomial involutions over finite fields

Explicit constructions of bent functions from pseudo-planar functions

Kanat Abdukhalikov^1,1, and
Sihem Mesnager^2,

1.
Department of Mathematical Sciences, UAE University, PO Box 15551, Al Ain, UAE
2.
Department of Mathematics, University of Paris VIII and Paris XIII and Télécom ParisTech, LAGA, UMR 7539, CNRS, Sorbonne Paris Cité

¹The first author was supported by UAEU grant 31S107.

Received: February 2016

Revised: March 2016

Published: September 2017

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Abstract

We investigate explicit constructions of bent functions which are linear on elements of spreads. Our constructions are obtained from symplectic presemifields which are associated to pseudo-planar functions. The following diagram gives an indication of the main interconnections arising in this paper: $pseudo-planar\ functions \longleftrightarrow\ commutaive\ presemifields \longrightarrow bent\ functions$

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Mathematics Subject Classification: 51E23, 12K10, 94A60.

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References

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