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Title: A new approach to determine the minimal polynomials of binary modified de Bruijn sequences
Authors: Musthofa
Indah Emilia Wijayanti
Diah Junia Eksi Palupi
Ezerman, Martianus Frederic
Keywords: Science::Mathematics
Issue Date: 2022
Source: Musthofa, Indah Emilia Wijayanti, Diah Junia Eksi Palupi & Ezerman, M. F. (2022). A new approach to determine the minimal polynomials of binary modified de Bruijn sequences. Mathematics, 10(15), 2577-.
Project: 04INS000047C230GRT01
Journal: Mathematics
Abstract: 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.
ISSN: 2227-7390
DOI: 10.3390/math10152577
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// 4.0/).
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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