Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic  

作　　者：ZHENG Dabin YU Long HU Lei 

机构地区：[1]Faculty of Mathematics and Statistics, Hubei University [2]School of Mathematics and Statistics, Central China Normal University [3]State Key Laboratory of Information Security, Institute of Information Engineering, CAS

出　　处：《Chinese Journal of Electronics》2014年第4期767-772,共6页电子学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11101131);the National Basic Research Program of China(No.2013CB834203)

摘　　要：Let n = me and p be an odd prime. Let Fp be a finite field and Fpn be its nth field extension. By some polynomial GCD computatlons, this paper characterize the hentness and semi-bentness of two classes of p-ary quadratic functions from Fp^n to Fp with coefficients in Fpe. Moreover, the enumeration formulas of constructed bent functions are obtained for some special cases of m. The results generalize some previous related work.Let n=me and p be an odd prime. Let Fp be a finite field and Fpn be its n th field extension. By some polynomial GCD computations, this paper characterize the bentness and semi-bentness of two classes of p-ary quadratic functions from Fpn to Fp with coefficients in Fpe. Moreover, the enumeration formulas of constructed bent functions are obtained for some special cases of m. The results generalize some previous related work.

关 键 词：Quadratic bent function  Quadratic semibent function Greatest common divisor  Block cyclic matrix. 

分 类 号：O175[理学—数学]