On existence of two symbol complete orthogonal arrays
type: Item
instance of: scholarly article
title: On existence of two symbol complete orthogonal arrays
zbMATH Open document ID: 0801.05015
DOI: 10.1016/0097-3165(94)90059-0
author: Rahul Mukerjee
author: Sanpei Kageyama
published in: Journal of Combinatorial Theory. Series A
publication date: 1994-11-27T00:00:00Z
review text: An orthogonal array \(\text{OA}(N,m,s,t)\) consists of an \(m\times N\) matrix \(A\) with entries from an \(s\)-set such that every \(t\times N\) submatrix of \(A\) contains \(\lambda\) copies of each \(t\times 1\) column vector, and so \(N= \lambda s^ t\). An orthogonal array that achieves Rao's bound is called complete. It is known (see the second author [J. Stat. Plann. Inference 19, No. 3, 395-400 (1988; Zbl 0655.05016)]) that a complete \(\text{OA}(N,m,2,t)\) exists whenever \(m= t+1\). The authors show that a complete \(\text{OA}(N,m,2,6)\) exists if and only if \(m= 7\) or 23 and that a complete \(\text{OA}(N,m,2,7)\) exists if and only if \(m= 8\) or 24. The existence for \(m= 23\) and 24 follows from the existence of the binary (23,12) Golay code. For \(8\leq t\leq 13\), the authors have checked that for \(m\leq 10^ 9\), a complete \(\text{OA}(N,m,2,t)\) exists only for \(m= t+1\). They conjecture that for \(t\geq 4\) with \(t\neq 6\) or 7, a complete \(\text{OA}(N,m,2,t)\) exists if and only if \(m= t+1\).
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 584023
zbMATH Keywords: orthogonal array
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90059-0
OpenAlex ID: W1969214470
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description: scientific article; zbMATH DE number 584023