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Hadamard matrices of order 36 with automorphisms of order 17

Published online by Cambridge University Press:  22 January 2016

Vladimir D. Tonchev
Vladimir D. Tonchev*
Affiliation:
Institute of Mathematics, Sofia 1090, P.O. Box 373, Bulgaria
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A Hadamard matrix of order n is an n by n matrix of 1’s and − 1’s such that HHt − nI. In such a matrix n is necessarily 1, 2 or a multiple of 4. Two Hadamard matrices H 1 and H 2 are called equivalent if there exist monomial matrices P, Q with PH 1 Q = H 2. An automorphism of a Hadamard matrix H is an equivalence of the matrix to itself, i.e. a pair (P, Q) of monomial matrices such that PHQ = H. In other words, an automorphism of H is a permutation of its rows followed by multiplication of some rows by − 1, which leads to reordering of its columns and multiplication of some columns by − 1. The set of all automorphisms form a group under composition called the automorphism group (Aut H) of H. For a detailed study of the basic properties and applications of Hadamard matrices see, e.g. [1], [7, Chap. 14], [8].

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 104 , December 1986 , pp. 163 - 174
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

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