Kasami Bent Functions are Not Equivalent to Their Duals
نویسندگان
چکیده
A difficult task in the theory of bent functions is to determine whether a bent function is equivalent to its dual bent function. In this paper we use certain results on the divisibility of Gauss Sums, mainly Stickelberger’s Theorem, to study monomial bent functions. We find the degree of the dual bent function of the Kasami function, which in general is different from the degree of the Kasami function itself. It follows that the Kasami bent functions are not equivalent to their duals in general.
منابع مشابه
On Kasami Bent Functions
It is proved that no non-quadratic Kasami bent is affine equivalent to MaioranaMacFarland type bent functions.
متن کاملBent functions and line ovals
In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also...
متن کاملNew infinite families of p-ary weakly regular bent functions
The characterization and construction of bent functions are challenging problems. The paper generalizes the constructions of Boolean bent functions by Mesnager [33], Xu et al. [40] and p-ary bent functions by Xu et al. [41] to the construction of p-ary weakly regular bent functions and presents new infinite families of p-ary weakly regular bent functions from some known weakly regular bent func...
متن کاملGold and Kasami-Welch functions, quadratic forms, and bent functions
We use elementary facts about quadratic forms in characteristic 2 to evaluate the sign of some Walsh transforms in terms of a Jacobi symbol. These results are applied to the Walsh transforms of the Gold and KasamiWelch functions. We prove that the Gold functions yield bent functions when restricted to certain hyperplanes. We also use the sign information to determine the dual bent function.
متن کاملOn Dillon's class H of bent functions, Niho bent functions and o-polynomials
One of the classes of bent Boolean functions introduced by John Dillon in his thesis is family H. While this class corresponds to a nice original construction of bent functions in bivariate form, Dillon could exhibit in it only functions which already belonged to the wellknown Maiorana-McFarland class. We first notice that H can be extended to a slightly larger class that we denote by H. We obs...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007