Further results on optimal optical orthogonal codes with weight 4.
type: Item
instance of: scholarly article
title: Further results on optimal optical orthogonal codes with weight 4.
zbMATH Open document ID: 1046.94015
DOI: 10.1016/S0012-365X(03)00264-4
author: Jianxing Yin
author: Yanxun Chang
published in: Discrete Mathematics
publication date: 2004-03-29T00:00:00Z
review text: A \((v,k,\lambda_a,\lambda_c)\) optical orthogonal code \({\mathcal C}\) (OOC) is a family of (0,1)-sequences with \(k\) 1's and \(v-k\) 0's satisfying the properties: (1) The auto-correlation property: \(\sum x_tx_{t+i}\leq\lambda_a\) for any \((x_0,\ldots,x_{v-1})\in{\mathcal C}\) and any integer \(i\not\equiv0\mod v\). (2) The cross-correlation property: \(\sum x_ty_{t+i}\leq\lambda_c\) for any two different sequences \((x_0,\ldots,x_{v-1}), (y_0,\ldots,y_{v-1})\in{\mathcal C}\) and any integer \(i\). In this paper, the authors prove the existence of optimal \((v,4,1)\)-OOC for \(v=3^nu\), where \(u\) is a product of primes congruent to 1 modulo 4, or \(v=2^nu\), where \(u\) is a product of primes congruent to 1 modulo 6.
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 94A55
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 2062784
zbMATH Keywords: optimal optical orthogonal codes
zbMATH Keywords: cyclic packings
zbMATH Keywords: auto-correlation
zbMATH Keywords: cross-correlation
reviewed by: I. Landjev
MaRDI profile type: Publication
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full work available at URL: s0012-365x(03)00264-4
OpenAlex ID: W1988514913
description: scientific article; zbMATH DE number 2062784