Bent sequence families are mainly generated by a linear onto mapping and a bent function.Nevertheless

for a long time

the linear onto mapping has not an explicit expression.Firstly analyzing the conditions that the linear onto mapping must obey

then based on the theory of finite field and the distribution of m?sequences

the explicit expression of linear onto mapping is obtained.Therefore the trace representation of Bent sequences is gotten.Finally a family of Bent sequences is constructed which can be rapidly generated by the trace representation of Bent sequences and some Bent functions.