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中文摘要：
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.
英文摘要：
A sufficient and necessary condition that a quadratic polynomial function is a bent function was presented by Ma W P,et al.in 2005.In the same year,Charpin P,et al proposed a sufficient and necessary condition that a polynomial function is a quadratic semi-Bent function with three trace terms in a paper.Corollary 5,6 of the former and Theorem 5,6 of the latter are not quite right by further investigating these conditions.Based on the theory of quadratic polynomial over finite fields,the correct conditions are presented.Moreover,some quadratic bent functions with three or four trace terms are constructed.Finally,a new method for constructing bent functions in polynomial forms is provided by using bent functions of two trace terms and permutation of polynomial.
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