Characterizations of generators for modified de Bruijn sequences
type: Item
instance of: scholarly article
title: Characterizations of generators for modified de Bruijn sequences
zbMATH Open document ID: 0787.11049
DOI: 10.1016/0196-8858(92)90021-N
author: Gregory L. Mayhew
author: S. W. Golomb
published in: Advances in Applied Mathematics
publication date: 1994-05-25T00:00:00Z
review text: Removing a single zero from the longest run of zeros in an order \(n\) de Bruijn sequence produces the corresponding order \(n\) modified de Bruijn sequence with the period \(2^ n-1\). The \(m\)-sequences, whose feedback function are primitive polynomials over \(GF(2)\) form a linear subset of modified de Bruijn sequences. This paper studies the nonlinear feedback function characteristics of the remaining order \(n\) modified de Bruijn sequences. These feedback functions have the form \(x_ n\oplus g(x_{n- 1},\dots,x_ 1)\) where \(\oplus\) denotes the addition over \(GF(2)\). The distribution data of the feedback function for \(4\leq n \leq b\) are presented. Some theoretical results about the weight, the number of terms and the degree of nonlinearity of the function \(g(x_{n-1},\dots,x_ 1)\) are also provided.
reviewed by: Dingyi Pei
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94A55
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 203285
zbMATH Keywords: weight
zbMATH Keywords: number of terms
zbMATH Keywords: degree of nonlinearity
zbMATH Keywords: nonlinear feedback function
zbMATH Keywords: modified de Bruijn sequences
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 203285