A Family of p-ary Binomial Bent Functions

Abstract

For a prime p with p ≡ 3 (mod 4) and an odd number m, the Bentness of the p-ary binomial function f a,b (x) = Tr n 1 (ax) is characterized, where n = 2m, a ∈ F * p n , and b ∈ F * p 2 . The necessary and sufficient conditions of f a,b (x) being Bent are established respectively by an exponential sum and two sequences related to a and b. For the special case of p = 3, we further characterize the Bentness of the ternary function f a,b (x) by the Hamming weight of a sequence.

Several New Classes of Bent Functions From Dillon Exponents

“…Therefore, we can obtain the following result according to the above discussions and the method used in [31].…”

“…This is the unique known -ary bent function of form (1) with . For the case , several classes of binomial functions can be found in [23] and [29] for and in [19] and [31] for , respectively. In this paper, for any prime , we give a necessary and sufficient condition concerning the bentness of defined by (1).…”

Three new infinite families of bent functions

“…These constructions divides into two categories: the primary constructions-giving bent functions from scratch, and the secondary ones-building new bent functions from one or several given bent functions. For an non-exhaustive list of references dealing with these two kinds of constructions, see [13][14][15][16][17][18][19][20][21][22][23][24]. On the other hand, every bent function has a dual function, which is a bent function as well.…”