Optimal and suboptimal quadriphase sequences derived from maximal length sequences over \(\mathbb{Z}_4\)
type: Item
instance of: scholarly article
title: Optimal and suboptimal quadriphase sequences derived from maximal length sequences over \(\mathbb{Z}_4\)
zbMATH Open document ID: 0921.94009
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1999-10-06T00:00:00Z
review text: Quadriphase sequences are studied with respect to their correlation properties. A quadriphase sequence is a sequence consisting of 4th roots of unity. A set of such sequences is called optimal if the maximum magnitude \(\theta_{\max}\) of the periodic crosscorrelation and out-of-phase auto-correlation meets the Welch bound, and suboptimal if \(\theta_{\max}\) is bounded by \(\sqrt{2L}\), where \(L\) is the length of the sequence. Quadriphase sequences are related to \(\mathbb{Z}_4\)-sequences by using the map \(x\to \omega^x\) where \(\omega\) is a 4th root of unity. It turns out that taking certain (interleaved) maximum length sequences over \(\mathbb{Z}_4\) one can get (suboptimal) quadriphase sequences. These maximum length sequences over \(\mathbb{Z}_4\) are constructed using the trace function from the Galois extension ring GR\((4,r)\) to \(\mathbb{Z}_4\). The correlation properties are obtained by examining the eigenvalues of an Abelian association scheme on GR\((4,r)\) and by using the linearity of the trace function.
Mathematics Subject Classification ID: 94A55
Mathematics Subject Classification ID: 11K45
zbMATH DE Number: 1195712
zbMATH Keywords: pseudorandom sequences
zbMATH Keywords: periodic correlation
zbMATH Keywords: quadriphase sequences
author: P. Udaya
author: Mohammad Umar Siddiqi
reviewed by: Herman J. Tiersma
MaRDI profile type: Publication
full work available at URL: s002000050101
OpenAlex ID: W2024470588
DOI: 10.1007/S002000050101
description: scientific article; zbMATH DE number 1195712