Construction of generalized binary Bent sequences

Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-essary condition is derived to determine whether the sum of the combinations of Gold functions,tr1^(n)(x^(2+1)),1≤i≤n−1,over finite fields 2n F(n be even)in addition to another term tr1^(n/2)(x^(2n/2+1))is a Bent function.Similar to the result presented by Khoo et al.,the condition can be verified by polynominal greatest common divisor(GCD)computation.A similar result also holds in the case n pF(n be even,p be odd prime).Using the constructed Bent functions and Niho type Bent functions given by Dobbertin et al.,many new generalized binary Bent sequences are obtained.