TY - JOUR
T1 - Cyclic Bent Functions and Their Applications in Sequences
AU - Abdukhalikov, Kanat
AU - Ding, Cunsheng
AU - Mesnager, Sihem
AU - Tang, Chunming
AU - Xiong, Maosheng
N1 - Funding Information:
Manuscript received September 29, 2019; revised January 29, 2021; accepted February 2, 2021. Date of publication February 8, 2021; date of current version May 20, 2021. The work of Kanat Abdukhalikov was supported by UAEU under Grant 31S366. The work of Cunsheng Ding was supported by The Hong Kong Research Grants Council under Grant 16300418. The work of Chunming Tang was supported by The National Natural Science Foundation of China under Grant 11871058. The work of Maosheng Xiong was supported by The Hong Kong Research Grants Council under Grant N_HKUST619/17. (Corresponding author: Chunming Tang.) Kanat Abdukhalikov is with the Department of Mathematical Sciences, UAE University, Al Ain 15551, UAE (e-mail: abdukhalik@uaeu.ac.ae).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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.
KW - Bent function
KW - code
KW - cyclic bent function
KW - prequasifield
KW - sequence
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U2 - 10.1109/TIT.2021.3057896
DO - 10.1109/TIT.2021.3057896
M3 - Article
AN - SCOPUS:85100864611
SN - 0018-9448
VL - 67
SP - 3473
EP - 3485
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
M1 - 9350302
ER -