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
Source: 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
Keywords: quasi-perfect sequence; difference set; character; Hadamard transform; multiplier group
Document URI: http://hdl.handle.net/1942/2020
Link to publication: http://www.worldscinet.com/cgi-bin/details.cgi?id=jsname:ac&type=all
ISSN: 1005-3867
e-ISSN: 0219-1733
ISI #: 000233566600011
Category: A1
Type: Journal Contribution
Validations: ecoom 2006
Appears in Collections:Research publications

Show full item record

Page view(s)

64
checked on May 18, 2022

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.