Construction of generalized binary Bent sequences

Abstract

Bent functions in trace forms play an important role in the constructions of generalized binary Bent sequences. Trace representation of some degree two Bent functions are presented in this paper. A sufficient and necessary condition is derived to determine whether the sum of the combinations of Gold functions, tr₁ⁿ (x²ⁱ⁺¹ ), 1≤i ≤n - 1, over finite fields F_2ⁿ (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 F_pⁿ ( 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.