Autocorrelation function of a family of complex sequences
type: Item
instance of: scholarly article
title: Autocorrelation function of a family of complex sequences
zbMATH Open document ID: 0817.94007
author: Chao Li
published in: Chinese Science Bulletin
publication date: 1995-08-08T00:00:00Z
review text: Starting with GMW sequences [IEEE Trans. Inf. Theory 30, 548-553 (1984; Zbl 0544.65005)] over \(GF (2^ k)\), generalized GMW sequences over \(GF (p^ k)\) for \(k= k_ 1 \cdot \dots \cdot k_ t\) are constructed by using trace functions of the field extensions \(GF (p^{k_ 1\cdot \dots\cdot k_ s} )\subseteq GF (p^{k_ 1\cdot \dots\cdot k_{s+1}})\) and a primitive element of \(GF (p^ k)\). It is shown that the complex sequences obtained in this way have optimal autocorrelation properties. Finally, statistical properties are stated and the number of generalized GMW sequences according to the choice of \(p\) and \(k_ 1,\dots, k_ t\) is given.
Mathematics Subject Classification ID: 94A55
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 646688
zbMATH Keywords: autocorrelation function
zbMATH Keywords: finite field
zbMATH Keywords: generalized GMW sequences
zbMATH Keywords: trace functions
zbMATH Keywords: optimal autocorrelation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 646688