Jurnal Natural
Jurnal Natural (J. Natural) is a premier, multidisciplinary, open-access journal dedicated to the rapid publication of high-quality, peer-reviewed research in the fields of mathematics, biological sciences, physics, chemistry, pharmacy, statistics, and informatics. Published by the Faculty of Mathematics and Natural Sciences at Universitas Syiah Kuala, Indonesia, J. Natural is committed to fostering the global exchange of scientific knowledge and ideas. J. Natural collaborate with some academic associations in Indonesia including IndoMS (Mathematics), HKI (Chemistry), PHI (Physics) and HAGI (Geophysics). The journal publishes three issues per year (February, June, and October) and welcomes submissions from researchers, scholars, and professionals worldwide. J. Natural focuses on a wide range of scientific scopes, including, but not limited to: Mathematics: Algebra, analysis, geometry, topology, and applied mathematics Biological Sciences: Cell biology, genetics, microbiology, molecular biology, biochemistry, biophysics, ecology, and evolution Physics: Classical and quantum mechanics, geophysics, statistical mechanics, electromagnetism, optics, and condensed matter physics Chemistry: Organic, inorganic, physical, analytical, and theoretical chemistry Pharmacy: Pharmaceutical chemistry, pharmacology, pharmacognosy, pharmaceutics, and clinical pharmacy Statistics: Mathematical statistics, biostatistics, statistical theory, and statistical methods Informatics: Computer science, artificial intelligence, data science, machine learning, and cybersecurity J. Natural is an entirely open-access journal, with a transparent and efficient blind review process that ensures the highest standards of quality and integrity. The journal applies a publishing charge for authors, ensuring the sustainability of the publication and the accessibility of the content for readers worldwide.
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Constructing modified binary de Bruijn sequences via cycle joining based on the prefer-complement algorithm
Musthofa Musthofa;
Agus Maman Abadi;
Karyati Karyati;
Lusi Harini
Jurnal Natural Vol. 26 No. 2 (2026)
Publisher : Faculty of Mathematics and Natural Science (FMIPA), Universitas Syiah Kuala
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DOI: 10.24815/jn.v26i2.407
This paper presents a generalized implementation of the cycle joining algorithm for generating binary sequences corresponding to modified de Bruijn sequences of order . The proposed approach can be interpreted in terms of a modified de Bruijn graph, where vertices represent binary strings of length and edges correspond to allowable transitions under the modification rules. The algorithm can be applied to any integer and can start from any chosen initial vertex. The procedure begins by constructing an initial sequence using the prefer-complement algorithm. The method can produce multiple disjoint cycles, which are iteratively extended and joined into a single sequence. A key challenge in cycle joining is identifying suitable conjugate pairs for merging cycles. In this approach, conjugate pairs are efficiently determined through the algorithm’s structured scheme, simplifying the joining process. The resulting sequence achieves the maximal length , which corresponds to a modified de Bruijn sequence. The flexibility of the algorithm allows it to accommodate varying initial vertices, making it highly adaptable for sequence generation. Its ability to systematically join multiple cycles into a single sequence corresponding to a modified de Bruijn sequence demonstrates potential applications in cryptographic keystream generation, pseudorandom binary sequence design, and other areas requiring structured yet complex binary sequences.