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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2020

Title: Quasi-perfect sequences and Hadamard difference sets
Authors: OOMS, Alfons
QIU, Weisheng
Issue Date: 2005
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
Citation: ALGEBRA COLLOQUIUM, 12(4). p. 635-644
Abstract: In this paper, we prove that a binary sequence is perfect (resp., quasi-perfect) if and only if its support set for any finite group (not necessarily cyclic) is a Hadamard difference set of type I (resp., type II); and we prove that the kernel of any nonzero linear functional (or the image of any linear transformation A with dim(Ker A) = 1) on the linear space GF(2(m)) over the field GF(2(m)) (excluding 0) is a cyclic Hadamard difference set of type II using Gaussian sums; and we prove that the multiplier group of the above difference set is equal to the Galois group Gal(GF(2(m))/GF(2)); and we mention the relationship between the Hadamard transform and the irreducible complex characters.
Notes: Univ Limburg, Dept Math, B-3590 Diepenbeek, Belgium. Peking Univ, Dept Math, LMAM, Beijing 100871, Peoples R China.Ooms, AI, Univ Limburg, Dept Math, B-3590 Diepenbeek, Belgium.alfons.ooms@luc.ac.be qiuws@pku.edu.cn
URI: http://hdl.handle.net/1942/2020
Link to publication: http://www.worldscinet.com/cgi-bin/details.cgi?id=jsname:ac&type=all
ISI #: 000233566600011
ISSN: 1005-3867
Category: A1
Type: Journal Contribution
Validation: ecoom, 2006
Appears in Collections: Research publications

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