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针对MaWP等给出的二次多项式函数是Bent函数的充要条件以及CharpinP等给出的二次三项函数是semi-Bent函数的充要条件这2个结论进行了研究,结果表明,MaWP等文章中的推论5、6和CharpinP等文章中的定理5、6是不完全正确的.结合有限域上的二次多项式理论,给出了相应的正确结果,并构造了一类三项式和四项式Bent函数.借助多项式置换,提出了一种利用二次二项Bent函数构造多项式Bent函数的新方法.
For MaWP and so on given quadratic polynomial function is Bent function of the necessary conditions and given CharpinP given quadratic function is semi-Bent necessary and sufficient conditions of these two conclusions were studied, the results show that MaWP and other The reasoning 5 and 6 in the article 5,6 and the CharpinP article is not entirely correct. Combined with the quadratic polynomial theory on the finite field, the corresponding correct results are given and a class of triadic and Quadratic Bent function. By means of polynomial permutation, a new method of constructing polynomial Bent function by quadratic B-Bent function is proposed.