Abstract
In this paper we give a new series of Hadamard matrices of order 2t. When the order is 16, Hadamard matrices obtained here belong to class II, class V or to class IV of Hall's classification [3]. By combining our matrices with the matrices belonging to class I, class II or class III obtained before, we can say that we have direct construction, namely without resorting to block designs, for all classes of Hadamard matrices of order 16.
Furthermore we show that the maximal excess of Hadamard matrices of order 22t is 23t, which was proved by J. Hammer, R. Levingston and J. Seberry [4]. We believe that our matrices are inequivalent to the matrices used by the above authors. More generally, if there is an Hadamard matrix of order 4n 2 with the maximal excess 8n 3, then there exist more than one inequivalent Hadamard matrices of order 22t n 2 with the maximal excess 23t n 3 for anyt ≧ 2.
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Yamada, M. On a series of Hadamard matrices of order 2t and the maximal excess of Hadamard matrices of order 22t . Graphs and Combinatorics 4, 297–301 (1988). https://doi.org/10.1007/BF01864168
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DOI: https://doi.org/10.1007/BF01864168