Linear complexity profile of \(m\)-ary pseudorandom sequences with small correlation measure
type: Item
instance of: scholarly article
title: Linear complexity profile of \(m\)-ary pseudorandom sequences with small correlation measure
zbMATH Open document ID: 1237.11034
DOI: 10.1016/S0019-3577(09)80030-X
author: Juan-Miguel Gracia
published in: Indagationes Mathematicae. New Series
publication date: 2011-03-31T00:00:00Z
review text: In [\textit{N. Brandstätter} and \textit{A. Winterhof}, Period. Math. Hungar. 52, 1--8 (2006; Zbl 1127.11050)] the linear complexity profile of a binary sequence is estimated in terms of the correlation measure of order \(l\) introduced by \textit{C. Mauduit} and \textit{A. Sarközy} in [Acta Arith. 82, 365--377 (1997; Zbl 0886.11048)]. The authors introduce a new correlation measure for sequences over \(\mathbb Z_m = \{0,1,\ldots,m-1\}\), which is applicable also for composite integers \(m\), and present a lower bound for the linear complexity profile over \(\mathbb Z_m\) of an \(m\)-ary sequence in terms of the new correlation measure. If \(m\) is not prime, then this generalization of the binary case is not straightforward. The result is then applied to obtain bounds on the linear complexity profile for sequences of discrete logarithms modulo \(m\), and for quaternary sequences derived from two Legendre sequences.
reviewed by: Wilfried Meidl
Mathematics Subject Classification ID: 11K36
Mathematics Subject Classification ID: 94A55
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 5872503
zbMATH Keywords: Linear complexity profile
zbMATH Keywords: correlation measure
zbMATH Keywords: \(m\)-ary sequence
zbMATH Keywords: quaternary sequence
zbMATH Keywords: discrete logarithm
zbMATH Keywords: Legendre sequence
MaRDI profile type: Publication
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full work available at URL: s0019-3577(09)80030-x
OpenAlex ID: W2027304562
description: scientific article; zbMATH DE number 5872503