A Family of p-ary Binomial Bent Functions

For a prime p with p ≡ 3(mod 4) and an odd number m, the Bentness of the p-ary binomial function $f_{a,b}(x)={\\ m Tr}_{1}^n(ax^{p^m-1})+{\\ m Tr}_{1}^2(bx^{\\frac{p^n-1}{4}})$ is characterized, where n=2m, $a\\in \\bF_{p^n}^*$, and $b\\in \\bF_{p^2}^*$. The necessary and sufficient conditions of ƒa,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 ƒa,b(x) by the Hamming weight of a sequence.

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