Cyclic Bent Functions and Their Applications in Sequences

Kanat Abdukhalikov, Cunsheng Ding, Sihem Mesnager, Chunming Tang, Maosheng Xiong

Research output: Contribution to journalArticlepeer-review

Abstract

Let m be an even positive integer. A Boolean bent function f on F2m-1 × F2is called a cyclic bent function if for any a neq b F2m-1 and F2,f(ax1,x2)+f(bx1,x2+) is always bent, where x1\inF2m}-1, x2 \in F2. Cyclic bent functions look extremely rare. This paper focuses on cyclic bent functions on F2m-1 × F2 and their applications. The first objective of this paper is to establish a link between quadratic cyclic bent functions and a special type of prequasifields, and construct a class of quadratic cyclic bent functions from the Kantor-Williams prequasifields. The second objective is to use cyclic bent functions to construct families of optimal sequences. The results of this paper show that cyclic bent functions have nice applications in several fields such as coding theory, symmetric cryptography, and CDMA communication.

Original languageEnglish
Article number9350302
Pages (from-to)3473-3485
Number of pages13
JournalIEEE Transactions on Information Theory
Volume67
Issue number6
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Bent function
  • code
  • cyclic bent function
  • prequasifield
  • sequence

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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