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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/dataset: | 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 |
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