A note on geometric structures of linear ordered orthogonal arrays and \((t,m,s)\)-nets of low strength
type: Item
instance of: scholarly article
title: A note on geometric structures of linear ordered orthogonal arrays and \((t,m,s)\)-nets of low strength
zbMATH Open document ID: 1001.05027
DOI: 10.1023/A:1016525813635
author: Ryoh Fuji-Hara
author: Ying Miao
published in: Designs, Codes and Cryptography
publication date: 2002-08-21T00:00:00Z
review text: Ordered orthogonal arrays are a large family of combinatorial objects, which contain orthogonal arrays and \((t,m,s)\)-nets as subclasses. A \(q\)-ary ordered orthogonal array is linear if it forms a vector space over the field with \(q\) elements. Each \((t,m,s)\)-net projects to an ordinary orthogonal array. The embedding problem asks if a given orthogonal array can be embedded in a \((t,m,s)\)-net. In the present paper well-known embedding theorems for linear orthogonal arrays (these are just the duals of linear error-correcting codes) in the case of strenghts 3 and 4 are reproved using geometric language.
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 11K45
zbMATH DE Number: 1785713
zbMATH Keywords: geometric structure
zbMATH Keywords: linear ordered orthogonal array
zbMATH Keywords: pseudo-random number generation
zbMATH Keywords: \((t,m,s)\)-net
zbMATH Keywords: theta configuration
zbMATH Keywords: orthogonal arrays
zbMATH Keywords: embedding theorems
reviewed by: Jürgen Bierbrauer
MaRDI profile type: Publication
full work available at URL: a:1016525813635
OpenAlex ID: W1500436934
description: scientific article; zbMATH DE number 1785713