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research
On Binary de Bruijn Sequences from LFSRs with Arbitrary Characteristic Polynomials
Authors
Zuling Chang
Martianus Frederic Ezerman
San Ling
Huaxiong Wang
Publication date
1 January 2018
Publisher
'Springer Science and Business Media LLC'
Doi
Cite
View
on
arXiv
Abstract
We propose a construction of de Bruijn sequences by the cycle joining method from linear feedback shift registers (LFSRs) with arbitrary characteristic polynomial
f
(
x
)
f(x)
f
(
x
)
. We study in detail the cycle structure of the set
Ω
(
f
(
x
)
)
\Omega(f(x))
Ω
(
f
(
x
))
that contains all sequences produced by a specific LFSR on distinct inputs and provide a fast way to find a state of each cycle. This leads to an efficient algorithm to find all conjugate pairs between any two cycles, yielding the adjacency graph. The approach is practical to generate a large class of de Bruijn sequences up to order
n
≈
20
n \approx 20
n
≈
20
. Many previously proposed constructions of de Bruijn sequences are shown to be special cases of our construction
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Digital Repository - Nanyang Technological University
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Last time updated on 16/04/2020
DR-NTU (Digital Repository of NTU)
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:dr.ntu.edu.sg:10356/103689
Last time updated on 02/08/2023