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Title: Quasi-perfect sequences and Hadamard difference sets
Authors: OOMS, Alfons 
QIU, Weisheng 
Issue Date: 2005
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,
Keywords: quasi-perfect sequence; difference set; character; Hadamard transform; multiplier group
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ISSN: 1005-3867
e-ISSN: 0219-1733
ISI #: 000233566600011
Category: A1
Type: Journal Contribution
Validations: ecoom 2006
Appears in Collections:Research publications

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