Starters and related codes
type: Item
instance of: scholarly article
title: Starters and related codes
zbMATH Open document ID: 0957.05018
DOI: 10.1016/S0378-3758(99)00119-6
author: N. Delaunay
published in: Journal of Statistical Planning and Inference
publication date: 2001-03-15T00:00:00Z
review text: The authors investigate skew starters and prove the existence of a skew starter in \(Z_v\) for all \(v\) such that \(\text{gcd}(v,6)= 1\), \(v\) is not divisible by 5 or \(v\) is divisible by 25. Next, they use skew starters to show the existence of an optimal \((6v,4,1)\) optical orthogonal code in \(Z_{6v}\) for all \(v\) such that \(\text{gcd}(v,6)= 1\). (A \((v,k,\rho)\) optical orthogonal code is a family of \((0,1)\)-sequences of length \(v\) and weight \(k\) satisfying both the auto-correlation property and the cross-correlation property.) Finally, the condition \(n\geq 8\) is proved to be necessary and sufficient for the existence of a constant weight code \((n,w,d)\) in \((Z_7)^n\) of length \(n\), minimum distance \(d= 3\), and constant Hamming weight \(w= 3\). (Frame starters are also used to prove this result).
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 94B25
zbMATH DE Number: 1471121
zbMATH Keywords: generalized Steiner triple systems
zbMATH Keywords: frame starters
zbMATH Keywords: skew starters
zbMATH Keywords: optical orthogonal code
zbMATH Keywords: constant weight code
MaRDI profile type: Publication
cites work: Q3737429
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cites work: Constant weight codes and group divisible designs
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full work available at URL: s0378-3758(99)00119-6
OpenAlex ID: W2086298232
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description: scientific article; zbMATH DE number 1471121