A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences

Autor:	Musthofa, Indah Emilia Wijayanti, Diah Junia Eksi Palupi, Martianus Frederic Ezerman
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	binary sequence Hamiltonian cycle linear span minimal polynomial modified de Bruijn sequence Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 15, p 2577 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10152577
Popis:	A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique least-degree characteristic polynomial. Leveraging a recent characterization, we devise a novel general approach to determine the minimal polynomial. We translate the characterization into a problem of identifying a Hamiltonian cycle in a specially constructed graph. The graph is isomorphic to the modified de Bruijn–Good graph. Along the way, we demonstrate the usefulness of some computational tools from the cycle joining method in the modified setup.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/23c2e026bac64e459653f38ec622cba6 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.