4-blocked Hadamard 3-designs
type: Item
instance of: scholarly article
title: 4-blocked Hadamard 3-designs
zbMATH Open document ID: 0889.05016
DOI: 10.1016/S0012-365X(96)00316-0
author: Luigia Berardi
author: Marco Buratti
author: Stefano Innamorati
published in: Discrete Mathematics
publication date: 1998-06-11T00:00:00Z
review text: A \(t\)-\((\nu,k, \lambda)\) design \(D\) is a pair \((V,B)\), where \(V\) is a set with \(\nu\) elements and \(B\) is a collection of \(k\)-subsets of \(V\) (called blocks), such that any subset of \(t\) elements of \(V\) appears in exactly \(\lambda\) blocks. A blocking \(c\)-set in \(D\) is a set \(C\) with \(c\) elements in it such that any block has in it a point of \(C\) and a point off \(C\). An Hadamard 3-design \(D_3\) of order \(n\) is a 3-\((4n, 2n,n-1)\) design whose existence is linked with the existence of an Hadamard matrix of size \(4n\). In this paper are investigated 4-blocked Hadamard 3-designs, i.e. Hadamard 3-designs that contain blocking 4-sets. The main result is as follows: Theorem. An Hadamard 3-design of odd order \(n\) is 4-blocked if and only if it contains a special \((n-1)\)-tuple. Moreover, if an Hadamard 3-design of even order \(n\) is 4-blocked, then it contains a special \(n\)-tuple. According to the above theorem the existence of blocking 4-sets is connected to the existence of special \(n\)-tuples or \((n-1)\)-tuples.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1110070
zbMATH Keywords: Hadamard 3-design
zbMATH Keywords: Hadamard matrix
zbMATH Keywords: existence
reviewed by: D. V. Chopra
MaRDI profile type: Publication
cites work: Q4004114
cites work: Q3754012
cites work: Q3826563
cites work: Q3790203
cites work: Q4505278
cites work: Q3686719
cites work: Non-isomorphic solutions of some balanced incomplete block designs. I
cites work: Q4001503
cites work: Q4004080
cites work: Blocking sets in block designs
cites work: Q3808107
cites work: Block Design Games
cites work: Constructing Steiner Triple Systems Partially Embedded in a Projective Plane
cites work: On Residue Difference Sets
cites work: On Orthogonal Matrices
cites work: A Combinatorial Problem
description: scientific article; zbMATH DE number 1110070