QQ客服 官方微博 反馈留言

	A method of evaluation of exponential sum of binary quadratic functions
	Zhang, Xiyong ; Cao, Xiwang ; Feng, Rongquan
	2012
关键词	Binary quadratic function Exponential sum Companion polynomial Reciprocal polynomial EXPLICIT EVALUATION
英文摘要	In this paper, by using the factorization of the companion polynomial of the binary quadratic function f(x) = Sigma(1 <= i <= k)aix(1+2ai) +aox, x is an element of F(2)n, a(i) is an element of F(2)m m vertical bar n we give a method to compute the exponential sum S(f, n) = Sigma(x is an element of)F(2)n (-1)(Tr(f(x))) for the quadratic functions f (x), where Tr(.) is the trace function from F(2)n to F-2. The computation of the exponential sum of quadratic functions with many terms can be transformed to that of some quadratic functions that can be explicitly evaluated by present results. Moreover, the necessary and sufficient condition for f'(z) equivalent to g(z) g*(z) (mod (2. z(2s) + 1)) is given, where g* (z) is the generalized reciprocal polynomial of g(z) and f '(z) is the companion polynomial of f (x). As a consequence, the exponential sums S ( f, 2(s)) for most binary quadratic functions f (x) is an element of F-2[x] can be computed. (c) 2012 Elsevier Inc. All rights reserved.; Mathematics, Applied; Mathematics; SCI(E); EI; 1; ARTICLE; 6; 1089-1103; 18
语种	英语
出处	SCI ; EI
出版者	finite fields and their applications
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/230557]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zhang, Xiyong,Cao, Xiwang,Feng, Rongquan. A method of evaluation of exponential sum of binary quadratic functions. 2012-01-01.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。