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	Finding normal bases over finite fields with prescribed trace self-orthogonal relations
	Zhang, Xiyong ; Feng, Rongquan ; Liao, Qunying ; Gao, Xuhong
	2014
关键词	Normal basis Self-dual Hamming weight Reciprocal polynomial Trace function DUAL NORMAL BASIS MULTIPLICATION CONSTRUCTION MULTIPLIERS COMPLEXITY
英文摘要	Normal bases and self-dual normal bases over finite fields have been found to be very useful in many fast arithmetic computations. It is well-known that there exists a self-dual normal basis of F-2(n) over F-2 if and only if 4 dagger n. In this paper, we prove that there exists a normal element alpha of F-2(n)= over F-2 corresponding to a prescribed vector a = (a(0), a(1), . . . , a(n-1)) is an element of F-2(n) such that a(i) = Tr-2(n)vertical bar 2(alpha(1+22)) for 0 <= i <= n - 1, where n is a 2-power or odd, if and only if the given vector a is symmetric (a(i) = a(n-i) for all i, 1 <= i <= n-1), and one of the following is true. [GRAPHICS] Furthermore we give an algorithm to obtain normal elements corresponding to prescribed vectors in the above two cases. For a general positive integer n with 4 vertical bar n, some necessary conditions for a vector to be the corresponding vector of a normal element of F-2(n) over F-2 are given. And for all n with 4 vertical bar n, we prove that there exists a normal element of F-2(n) over F-2 such that the Hamming weight of its corresponding vector is 3, which is the lowest possible Hamming weight. (C) 2014 Elsevier Inc. All rights reserved.; Mathematics, Applied; Mathematics; SCI(E); EI; 0; ARTICLE; xiyong.zhang@hotmail.com; 1-21; 28
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/20.500.11897/211302]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zhang, Xiyong,Feng, Rongquan,Liao, Qunying,et al. Finding normal bases over finite fields with prescribed trace self-orthogonal relations. 2014-01-01.

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