On a class of binomial bent functions over the finite fields of odd characteristic
Tóm tắt
We give a necessary and sufficient condition such that the class of
$$p$$
-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case
$$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1$$
for some even integers
$$t$$
and
$$n$$
. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones.
Tài liệu tham khảo
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