Hadamard matrices of order \(\equiv{} 8\)(mod 16) with maximal excess (Q1182935)
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scientific article; zbMATH DE number 32460
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hadamard matrices of order \(\equiv{} 8\)(mod 16) with maximal excess |
scientific article; zbMATH DE number 32460 |
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Hadamard matrices of order \(\equiv{} 8\)(mod 16) with maximal excess (English)
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28 June 1992
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The excess of a Hadamard matrix \(H\), denoted \(\sigma(H)\), is the sum of all its elements. \(\sigma(n)\) is used to denote the maximal excess of all Hadamard matrices of order \(n\). In this paper a new family of Hadamard matrices whose excess is maximal is given. It is shown that there is a Hadamard matrix of order \(4m(m-1)\) \((\equiv 0\pmod{16}\) and \(\equiv 8\pmod{16}\), respectively) whose excess meets the Kounias-Farmakis bound, i.e. \(\sigma(4m(m-1))=4(m-1)^ 2(2m+1)\).
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Hadamard matrices
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maximal excess
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Kounias-Farmakis bound
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