A Family of p-ary Binomial Bent Functions
For a prime p with p equivalent to 3 (mod 4) and an odd number m, the Bentness of the p-ary binomial function f(a,b(x)) = Tr(1)(n)(ax(pm-1)) + Tr(1)(2)(bx(pn-1/4)) is characterized, where n = 2m, a is an element of F*(pn), and b is an element of F*(p2). 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.
p-ary binomial bent functions exponential sum hamming weight