A new family of supplementary difference sets and Hadamard matrices
type: Item
instance of: scholarly article
title: A new family of supplementary difference sets and Hadamard matrices
zbMATH Open document ID: 0851.05027
DOI: 10.1016/0378-3758(95)00092-5
author: Gang Liu
author: Mingyuan Xia
published in: Journal of Statistical Planning and Inference
publication date: 1996-09-05T00:00:00Z
review text: The authors [J. Comb. Theory, Ser. A 58, No. 2, 310-317 (1991; Zbl 0758.05032)] showed that for any prime power \(q\equiv 1\pmod 4\) there exist \(4\)-\(\{v; k, k, k, k; \lambda\}\) supplementary difference sets with \(v= q^2\), \(k= q(q- 1)/2\), \(\lambda= 4k- v\) (difference sets \(D_1\), \(D_2\), \(D_3\), \(D_4\) are called \(4\)-\(\{v; k, k, k, k; \lambda\}\) supplementary if their elements are residues \(\text{mod } v\) and their parameters are of the form \((v, k, \lambda)\)). In this paper, the same authors prove that there exist \(4\)-\(\{v; k, k, k, k; \lambda\}\) supplementary difference sets with \(v= q^2\), \(q\equiv 3\pmod 8\) a prime power, \(k= q(q- 1)/2\), \(\lambda= 4k- v\) and Hadamard matrices of order \(4v\).
reviewed by: K.Burian
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 906667
zbMATH Keywords: supplementary difference sets
zbMATH Keywords: Hadamard matrices
MaRDI profile type: Publication
full work available at URL: 0378-3758(95)00092-5
OpenAlex ID: W2075761318
cites work: Q3715120
cites work: A family of supplementary difference sets
cites work: On supplementary difference sets
cites work: Nonexistence of certain supplementary difference sets
cites work: An infinite class of supplementary difference sets and Williamson matrices
cites work: Supplementary difference sets and Jacobi sums
description: scientific article; zbMATH DE number 906667