Generalized GMW quadriphase sequences satisfying the Elch bound with equality
type: Item
instance of: scholarly article
title: Generalized GMW quadriphase sequences satisfying the Elch bound with equality
zbMATH Open document ID: 0983.94028
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 2001-10-23T00:00:00Z
review text: This paper gives new families of quadriphase sequences obtained from large linear complexity sequences over \(\mathbb{Z}_4\) by making use of generalized permutation monomials over Galois rings. The construction of these sequences can be seen as a generalization of the binary GMW sequence construction, and hence they are referred to as GGMW sequences over \(\mathbb{Z}_4\). The GGMW families satisfy the Welch bound on inner products with equality, and it is shown that the root mean square of all the crosscorrelations and out-of-phase autocorrelations \((\theta_{\text{rms}})\) is approximately equal to the quantity \(\sqrt L; L\) being the period of the sequences. However, \(\theta_{\text{max}}\), the maximum magnitude of periodic crosscorrelation and out-of-phase autocorrelation, deviates from the optimal value of \(\sqrt L\). Computer results suggest that the number of crosscorrelation values which deviate from the optimal value of \(\sqrt L\) is small. The weight structure of these sequences is the same as those of \(m\)-sequences over \(\mathbb{Z}_4\). The linear complexity (LC) of the sequences is computed using a generalized Blahuts theorem on the LC of sequences over \(\mathbb{Z}_4\).
Mathematics Subject Classification ID: 94A55
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 1441261
zbMATH Keywords: quadriphase sequences
zbMATH Keywords: large linear complexity sequences
zbMATH Keywords: binary GMW sequence
zbMATH Keywords: Welch bound
zbMATH Keywords: crosscorrelation
zbMATH Keywords: out-of-phase autocorrelation
author: P. Udaya
author: Mohammad Umar Siddiqi
MaRDI profile type: Publication
full work available at URL: s002000050125
OpenAlex ID: W2009235680
DOI: 10.1007/S002000050125
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description: scientific article; zbMATH DE number 1441261