中文摘要：

Bent函数在编码理论、通信领域以及密码学中具有广泛的应用。文章利用二次型理论构造了定义在奇特征域Fpn上的二次Bent函数∑i=1^m/2-1ciTr1^n（βx^1＋pei）＋cm/2Tr1^n/2（βx1＋p^n/2）,其中。p是奇素数，ci∈Fp，n=em,且满足m是偶数；给出了这类函数是p-aryBent的充分必要条件。进一步地，当m=2p^vq，v≥0，q是一个奇素数且满足p是模q的原根，给出了这种情况下的此类二次Bent函数的个数。

英文摘要：

Bent functions are widely used in the fields of coding theory, communications and cryptog-raphy. This paper constructs a class of quadratic bent functions having the form ∑i=1^m/2-1ciTr1^n（βx^1＋pei）＋cm/2Tr1^n/2（βx1＋p^n/2）for even n with n = em,ci E Fp over the finite field of Fp~ of odd characteristic p by using the theory of quadratic forms over finite fields. Moreover, the necessary and sufficient con- ditions are presented. Further, when m = 2p~q,v 〉I O,q is an odd prime and p a primitive root mod- ulo q. The enumerations of this class of bent functions are also considered.