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On the classification of Hadamard matrices of order 32
Author(s) -
Kharaghani H.,
TayfehRezaie B.
Publication year - 2010
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20245
Subject(s) - hadamard transform , complex hadamard matrix , mathematics , hadamard's maximal determinant problem , hadamard matrix , hadamard's inequality , combinatorics , equivalence (formal languages) , hadamard product , order (exchange) , hadamard three lines theorem , type (biology) , discrete mathematics , mathematical analysis , ecology , finance , economics , biology
Abstract All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13, 680, 757 Hadamard matrices of one type and 26, 369 such matrices of another type. Based on experience with the classification of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insignificant. © 2009 Wiley Periodicals, Inc. J Combin Designs 18:328–336, 2010