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Title: An efficiently generated family of binary de Bruijn sequences
Authors: Zhu, Yunlong
Chang, Zuling
Ezerman, Martianus Frederic
Wang, Qiang
Keywords: Science::Mathematics
Issue Date: 2021
Source: Zhu, Y., Chang, Z., Ezerman, M. F. & Wang, Q. (2021). An efficiently generated family of binary de Bruijn sequences. Discrete Mathematics, 344(6), 112368-.
Journal: Discrete Mathematics
Abstract: We study how to generate binary de Bruijn sequences efficiently from the class of simple linear feedback shift registers with feedback function f (x0,x1, ...xn-1) = x0 +x1 +xn-1 for n >_ 3, using the cycle joining method. Based on the properties of this class of LFSRs, we propose two new generic successor rules, each of which produces at least 2n-3 de Bruijn sequences. These two classes build upon a framework proposed by Gabric, Sawada,Williams andWong in Discrete Mathematics vol. 341, no. 11, pp. 2977–2987, November 2018. Here we introduce new useful choices for the uniquely determined state in each cycle to devise valid successor rules. In each class, the next bit costs O(n) time and O(n) space for a fixed n.
ISSN: 0012-365X
DOI: 10.1016/j.disc.2021.112368
Schools: School of Physical and Mathematical Sciences 
Rights: © 2021 Elsevier B.V. All rights reserved. This paper was published in Discrete Mathematics and is made available with permission of Elsevier B.V.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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