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Construction of generalized binary Bent sequences |
| KE Pin-hui1, KE Pin-hui1, CHANG Zu-ling2, CHANG Zu-ling2, WEN Qiao-yan3, WEN Qiao-yan3 |
| 1.School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China; School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China; 2.State Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing 100039, China; Department of Mathematics, Zhengzhou University, Zhengzhou 450025, China; 3.School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China; |
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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 F2n (n be even) in addition to another term tr1n/2 (x2n/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 Fpn ( 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.
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Issue Date: 05 September 2006
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