On a class of almost perfect sequences
type: Item
instance of: scholarly article
title: On a class of almost perfect sequences
zbMATH Open document ID: 0880.05019
author: K. T. Arasu
author: N. J. Voss
author: Siu Lun Ma
published in: Journal of Algebra
publication date: 1998-01-14T00:00:00Z
review text: An \(n\)-periodic sequence \((s_i)\) with entries \(\pm1\) is almost perfect if all but one of the sums \(\sum^{n-1}_{i=0} s_is_{i+1}\) (\(t\not\equiv 0\pmod n\)) are zero. Any almost perfect sequence is equivalent to a cyclic difference set in \(\mathbb{Z}_n\) of size \(k={n\over 2}-\theta\) and \(\lambda_1=\theta(\theta-1)\), \(\lambda_2={n\over 4}-\theta\). The paper proves some necessary conditions for the existence of such difference sets and sequences. In particular, it is shown that if \(\theta=2\), there are only 6 possible values for \(n\) in the range \(n\leq 20,000\).
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 1038260
zbMATH Keywords: almost perfect sequence
zbMATH Keywords: cyclic difference set
reviewed by: Vladimir D. Tonchev
MaRDI profile type: Publication
full work available at URL: jabr.1997.6962
OpenAlex ID: W2068092142
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DOI: 10.1006/JABR.1997.6962
description: scientific article; zbMATH DE number 1038260