Title :
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
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2009.2030465
