广义bent序列的构造

Construction of generalized binary bent sequences

首先给出了一些二次bent函数在2nF上的迹函数的表示,考虑了有限域2nF(n为偶数)上Gold函数1(21)trnxi+,1≤i≤n?1,在F2上的线性组合,添加一项22211()nntrx+后所得函数构成bent函数的充分必要条件,类似于Khoo等人给出的结果,可以通过计算多项式的最大公因式来验证这个条件,并把这个结论推广到Fpn(n为偶数,p为奇素数)的情形。最后利用得到的结果以及Dobbertin等人构造的Niho型bent函数构造了新的广义bent序列。

Trace presentations of some twice degree bent functions were presented. A sufficient and necessary condition was derived to determine whether the sum of the combinations of Gold functions, tr1^n （x^2i＋1）, 1≤i≤n - 1, over finite fields F2^n （n be even） and another term tr1n/2＋1（x2n/2＋1）was bent function. Similar to the result given by Khoo et al., the condition can be verified by a polynominal GCD computation. A similar result is also hold in the case Fp^n（n be even, p be oddprime）. Using the constructed bent functions and Niho type bent functions given by Dobbertin et al., many new generalized binary bent sequences are obtained.