Bent functions and line ovals

Kanat Abdukhalikov

doi:10.1016/j.ffa.2017.06.002

Bent functions and line ovals

Kanat Abdukhalikov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also show that bent functions which are linear on elements of inequivalent spreads can be EA-equivalent.

Original language	English
Pages (from-to)	94-124
Number of pages	31
Journal	Finite Fields and their Applications
Volume	47
DOIs	https://doi.org/10.1016/j.ffa.2017.06.002
Publication status	Published - Sept 2017

Keywords

Bent functions
Line ovals
Niho bent functions
Ovals
Quasifields
Semifields
Spreads

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
Engineering(all)
Applied Mathematics

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10.1016/j.ffa.2017.06.002

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title = "Bent functions and line ovals",

abstract = "In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also show that bent functions which are linear on elements of inequivalent spreads can be EA-equivalent.",

keywords = "Bent functions, Line ovals, Niho bent functions, Ovals, Quasifields, Semifields, Spreads",

author = "Kanat Abdukhalikov",

note = "Funding Information: This work was supported by UAEU grant 31S107. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

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language = "English",

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AU - Abdukhalikov, Kanat

PY - 2017/9

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N2 - In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also show that bent functions which are linear on elements of inequivalent spreads can be EA-equivalent.

AB - In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also show that bent functions which are linear on elements of inequivalent spreads can be EA-equivalent.

KW - Bent functions

KW - Line ovals

KW - Niho bent functions

KW - Ovals

KW - Quasifields

KW - Semifields

KW - Spreads

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VL - 47

SP - 94

EP - 124

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Bent functions and line ovals

Abstract

Keywords

ASJC Scopus subject areas

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