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The 3-class Association Schemes Connected with Checkered Hadamard Matrices of Order 16

Authors
Journal
European Journal of Combinatorics
0195-6698
Publisher
Elsevier
Publication Date
Volume
21
Issue
7
Identifiers
DOI: 10.1006/eujc.2000.0404

Abstract

Abstract In this paper we determine all symmetric and non-symmetric 3-class association schemes such that for their adjacency matrices D i we have D 0 + D 3 = I 4 ⊗ J 4and D 0 + D 1 − D 2 + D 3is a checkered Hadamard matrix of order 16 (i.e. an Hadamard matrix consisting of 16 square blocks H ij of order 4 such that H ii = J 4and H ij J 4 = J 4 H ij = 0). It appears that there are, essentially, four symmetric and two non-symmetric 3-class association schemes of this kind.

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