15 research outputs found
On Greedy Algorithms for Binary de Bruijn Sequences
We propose a general greedy algorithm for binary de Bruijn sequences, called
Generalized Prefer-Opposite (GPO) Algorithm, and its modifications. By
identifying specific feedback functions and initial states, we demonstrate that
most previously-known greedy algorithms that generate binary de Bruijn
sequences are particular cases of our new algorithm
The Cycle Structure of LFSR with Arbitrary Characteristic Polynomial over Finite Fields
We determine the cycle structure of linear feedback shift register with
arbitrary monic characteristic polynomial over any finite field. For each
cycle, a method to find a state and a new way to represent the state are
proposed.Comment: An extended abstract containing preliminary results was presented at
SETA 201
On Binary de Bruijn Sequences from LFSRs with Arbitrary Characteristic Polynomials
We propose a construction of de Bruijn sequences by the cycle joining method
from linear feedback shift registers (LFSRs) with arbitrary characteristic
polynomial . We study in detail the cycle structure of the set
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 . Many previously
proposed constructions of de Bruijn sequences are shown to be special cases of
our construction
Rates of DNA Sequence Profiles for Practical Values of Read Lengths
A recent study by one of the authors has demonstrated the importance of
profile vectors in DNA-based data storage. We provide exact values and lower
bounds on the number of profile vectors for finite values of alphabet size ,
read length , and word length .Consequently, we demonstrate that for
and , the number of profile vectors is at least
with very close to one.In addition to enumeration
results, we provide a set of efficient encoding and decoding algorithms for
each of two particular families of profile vectors
Untersuchung von Qualifikationsmoeglichkeiten des Ionenbetriebwerkes RIT10 Schlussbericht
SIGLETIB Hannover: RN 4495(136) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman
An efficiently generated family of binary de Bruijn sequences
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.Nanyang Technological UniversityAccepted versionNanyang Technological University, Singapore Grant Number M4080456 supports the work of M. F. Ezerman