Skew-Hadamard matrices and the Smith normal form
type: Item
instance of: scholarly article
title: Skew-Hadamard matrices and the Smith normal form
zbMATH Open document ID: 0891.15006
DOI: 10.1023/A:1008230429804
author: T. S. Michael
author: Walter D. Wallis
published in: Designs, Codes and Cryptography
publication date: 1998-07-08T00:00:00Z
review text: The authors show that a skew-Hadamard (s-H) matrix of order \(4m\) has the Smith normal form (Snf): \[ \text{diag}\Biggl\{1,\underbrace{2,\dots,2}_{2m- 1},\underbrace{2m,\dots,2m}_{2m- 1},4m\Biggr\}. \] The Snf of the incidence matrix of an s-H \((4m-1, 2m,m)\)-design and of the (complementary) s-H \((4m-1,2m-1,m-1)\)-design are: \[ \text{diag}\Biggl\{\underbrace{1, \dots,1}_{2m- 1}, \underbrace{m,\dots, m}_{2m- 1},2m\Biggr\} \] and \[ \text{diag}\Biggl\{\underbrace{1,\dots, 1}_{2m}, \underbrace{m,\dots, m}_{2m- 2},m(2m- 1)\Biggr\}, \] respectively.
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1115736
zbMATH Keywords: skew-Hadamard matrix
zbMATH Keywords: design
zbMATH Keywords: Smith normal form
zbMATH Keywords: incidence matrix
reviewed by: Mihail Voicu
MaRDI profile type: Publication
full work available at URL: a:1008230429804
OpenAlex ID: W1578838308
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description: scientific article; zbMATH DE number 1115736