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, \(tr_1^n (x^{2^i + 1} )\), 1≤i≤n−1, over finite fields \(F_{2^n } \) (n be even) in addition to another term \(tr_1^{n/2} (x^{2n/2 + 1} )\) 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 \(F_{p^n } \) (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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Frontiers of Electrical and Electronic Engineering in China
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
