Hadamard matrices generated by an adaptation of generalized quaternion type array
type: Item
instance of: scholarly article
title: Hadamard matrices generated by an adaptation of generalized quaternion type array
zbMATH Open document ID: 0591.05013
DOI: 10.1007/BF01788091
author: Mieko Yamada
published in: Graphs and Combinatorics
publication date: 1986-01-01T00:00:00Z
review text: Let L denote the ring of generalized quaternions. Then the so-called right regular representation matrix of a particular element of L gives rise to a Hadamard matrix of order 2n of generalized quaternion type (GQT). The author establishes the existence of a Hadamard matrix of order \(4(n+1)\) which is an adaptation of GQT arrays. Similar theorems have been obtained by \textit{E. Spence} [J. Comb. Theory, Ser. A 19, 287-300 (1975; Zbl 0316.05018)] and \textit{A. L. Whiteman} [J. Number Theory 8, 1-11 (1976; Zbl 0329.05014)] by means of Goethals-Seidel arrays. The main result of the paper under review reads as follows. If \(q\equiv 1 (mod 4)\) and q-2 are prime numbers, then there exists a Hadamard matrix of order 4q. As an important tool of the proof, relative Gauß sums over a finite field are studied.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 11L10
Mathematics Subject Classification ID: 11A07
zbMATH DE Number: 3948283
zbMATH Keywords: generalized quaternion type arrays
zbMATH Keywords: Hadamard matrix
zbMATH Keywords: GQT
zbMATH Keywords: Goethals-Seidel arrays
zbMATH Keywords: relative Gauß sums
MaRDI profile type: Publication
cites work: Q3322113
cites work: Hadamard matrices from relative difference sets
cites work: Hadamard matrices of order 4(2p+1)
cites work: Hadamard matrices of generalized quaternion type
cites work: Williamson Hadamard matrices and Gauss sums
cites work: Q3772323
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description: scientific article; zbMATH DE number 3948283