中文摘要：

利用二次函数伴随多项式的一种特定分解形式,结合Frobenius变换和有限域上迹函数的性质,将一类二次函数的指数和转化为目前可计算的形式。并给出一种简化二次函数指数和计算的新方法。

英文摘要：

Factorizing the companion polynomials of binary quadratic function into the product of a polynomial and its reciprocal polynomial. With the property of the trace function and the Frobenius permutation, the exponential sums of a large class of quadratic functions with many terms can be converted to the computation of the exponential sums of some quadratic functions that can be explicitly evaluated by present results. A new method is also given to simplify the evaluation of exponential sums of these binary quadratic functions.