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

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 $f(x)$. We study in detail the cycle structure of the set $\Omega(f(x))$ 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 $n \approx 20$. Many previously proposed constructions of de Bruijn sequences are shown to be special cases of our construction

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

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 $q$, read length $\ell$, and word length $n$.Consequently, we demonstrate that for $q\ge 2$ and $n\le q^{\ell/2-1}$, the number of profile vectors is at least $q^{\kappa n}$ with $\kappa$ 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