493 research outputs found
On a conjecture of Helleseth
We are concern about a conjecture proposed in the middle of the seventies by
Hellesseth in the framework of maximal sequences and theirs cross-correlations.
The conjecture claims the existence of a zero outphase Fourier coefficient. We
give some divisibility properties in this direction
On a Conjecture of Helleseth
Abstract. We are concerned about a conjecture proposed in the middle of the seventies by Hellesseth in the framework of maximal sequences and theirs cross-correlations. The conjecture claims the existence of a zero outphase Fourier coefficient. We give some divisibility properties in this direction
Divisibility of Weil Sums of Binomials
Consider the Weil sum , where is
a finite field of characteristic , is the canonical additive
character of , is coprime to , and . We say that
is three-valued when it assumes precisely three distinct values as
runs through : this is the minimum number of distinct values in the
nondegenerate case, and three-valued are rare and desirable. When
is three-valued, we give a lower bound on the -adic valuation of
the values. This enables us to prove the characteristic case of a 1976
conjecture of Helleseth: when and is a power of ,
we show that cannot be three-valued.Comment: 11 page
Proofs of two conjectures on ternary weakly regular bent functions
We study ternary monomial functions of the form f(x)=\Tr_n(ax^d), where
x\in \Ff_{3^n} and \Tr_n: \Ff_{3^n}\to \Ff_3 is the absolute trace
function. Using a lemma of Hou \cite{hou}, Stickelberger's theorem on Gauss
sums, and certain ternary weight inequalities, we show that certain ternary
monomial functions arising from \cite{hk1} are weakly regular bent, settling a
conjecture of Helleseth and Kholosha \cite{hk1}. We also prove that the
Coulter-Matthews bent functions are weakly regular.Comment: 20 page
- …