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Classification of Hadamard matrices of order 28 with hall sets

โœ Scribed by Hiroshi Kimura

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
525 KB
Volume
128
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

We constructed 480 inequivalent Hadamard matrices with Hall sets of order 28 in Kimura (1988) and Kimura and Ohmori (1987). These matrices were classified by K-matrices and K-boxes associated with Hadamard matrices. In this paper we introduce some order on subsets of equivalence classes. By choosing maximal or minimal elements of these subsets, we get a complete classification and obtain 486 inequivalent matrices of order 28 with Hall sets.

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We constructed all inequivalent Hadamard matrices with Hall sets of order 28 and classified by K-matrices associated with Hadamard matrices except five matrices in our earlier work (Kimura, 1988) (see also Kimura, to appear;Kimura and Ohmori, 1987). In this paper we prove that Hadamard matrices with

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## 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