The combinatorics of binary arrays
type: Item
instance of: scholarly article
title: The combinatorics of binary arrays
zbMATH Open document ID: 0881.05025
DOI: 10.1016/S0378-3758(97)84208-5
author: M. García
published in: Journal of Statistical Planning and Inference
publication date: 1998-01-15T00:00:00Z
review text: This paper is a summary of a survey on (periodical binary) \(r\times s\) arrays, that is on infinite matrices \(A=\{a_{ij}\}\) (\(a_{ij}\in \{0,1\}\); \(i,j\) integers) such that \(a_{ij}=a_{i+r,s}=a_{i,j+s}\), for all \(i\) and \(j\). As generalisation of de Bruijn sequences is treated the possibility to have an \(r\times s\) array with \(rs=2^{mn}\) in which all \(m\times n\) subarrays are different. Certain autocorrelation functions for \(A\) give problems equivalent to questions on (relative or not) difference sets and planar functions and so lead for example to the projective plane conjecture. Other analogous functions lead for example to SONAR arrays, the Goulomb conjecture and Barker sequences. Obviously the paper can only point out some links and some (updated) references.
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 12E20
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 1057371
zbMATH Keywords: binary arrays
zbMATH Keywords: autocorrelation
zbMATH Keywords: difference sets
zbMATH Keywords: de Bruijn sequences
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
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