A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences
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 characte...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI
2022
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| Online Access: | https://repository.ugm.ac.id/278600/1/Wijayanti_MA.pdf |
| _version_ | 1826050286627586048 |
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| author | Musthofa, Musthofa Wijayanti, Indah Emilia Palupi, Diah Junia Eksi Ezerman, Martianus Frederic |
| author_facet | Musthofa, Musthofa Wijayanti, Indah Emilia Palupi, Diah Junia Eksi Ezerman, Martianus Frederic |
| author_sort | Musthofa, Musthofa |
| collection | UGM |
| description | 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. |
| first_indexed | 2024-03-14T00:01:29Z |
| format | Article |
| id | oai:generic.eprints.org:278600 |
| institution | Universiti Gadjah Mada |
| language | English |
| last_indexed | 2024-03-14T00:01:29Z |
| publishDate | 2022 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:generic.eprints.org:2786002023-11-02T02:33:47Z https://repository.ugm.ac.id/278600/ A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences Musthofa, Musthofa Wijayanti, Indah Emilia Palupi, Diah Junia Eksi Ezerman, Martianus Frederic Applied Mathematics Mathematics and Applied Sciences 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. MDPI 2022-07-25 Article PeerReviewed application/pdf en https://repository.ugm.ac.id/278600/1/Wijayanti_MA.pdf Musthofa, Musthofa and Wijayanti, Indah Emilia and Palupi, Diah Junia Eksi and Ezerman, Martianus Frederic (2022) A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences. Mathematics, 10 (2022). pp. 1-18. ISSN 2227-7390 https://www.mdpi.com/journal/mathematics https://doi.org/10.3390/math10152577 |
| spellingShingle | Applied Mathematics Mathematics and Applied Sciences Musthofa, Musthofa Wijayanti, Indah Emilia Palupi, Diah Junia Eksi Ezerman, Martianus Frederic A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences |
| title | A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences |
| title_full | A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences |
| title_fullStr | A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences |
| title_full_unstemmed | A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences |
| title_short | A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences |
| title_sort | new approach to determine the minimal polynomials of binary modified de bruijn sequences |
| topic | Applied Mathematics Mathematics and Applied Sciences |
| url | https://repository.ugm.ac.id/278600/1/Wijayanti_MA.pdf |
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