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|Title:||Quasi-perfect sequences and Hadamard difference sets||Authors:||OOMS, Alfons
|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.firstname.lastname@example.org email@example.com||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|
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