Proofs of Two Conjectures on Ternary Weakly Regular Bent Functions

Author

Helleseth, Tor ; Hollmann, Henk D L ; Kholosha, Alexander ; Wang, Zeying ; Xiang, Qing

Author_Institution

Dept. of Inf., Univ. of Bergen, Bergen, Norway

Volume

55

Issue

11

fYear

2009

Firstpage

5272

Lastpage

5283

Abstract

In this paper, we study ternary monomial functions of the form f(x) = Trn(axd), where x isin BBF ₃ n and Trn: BBF ₃ nrarr BBF ₃ is the absolute trace function. Using a lemma of Hou, Stickelberger´s theorem on Gauss sums, and certain ternary weight inequalities, we show that certain ternary monomial functions arising in the 2006 IEEE Transactions on Information Theory paper (vol. 52, pp. 2018-2032, 2006) are weakly regular bent, thus settling a conjecture of Helleseth and Kholosha. We also prove that the Coulter-Matthews bent functions are weakly regular.

Keywords

Gaussian processes; nonlinear functions; set theory; Coulter-Matthews bent functions; Gauss sums; Stickelberger´s theorem; absolute trace function; lemma of Hou; ternary monomial functions; ternary weakly regular bent functions; Councils; Galois fields; Gaussian processes; Informatics; Laboratories; Polynomials; Bent function; Gauss sum; Walsh transform; perfect nonlinear function; planar function; weakly regular bent function;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2009.2030465

Filename

5290285