On a Small Class of Binary Modified de Bruijn Sequences of Maximal Linear Span

Musthofa; Indah Emilia Wijayanti; Diah Junia Eksi Palupi; Martianus Frederic Ezerman

doi:10.1109/ICoCICs58778.2023.10276931

On a Small Class of Binary Modified de Bruijn Sequences of Maximal Linear Span

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Musthofa, Indah Emilia Wijayanti, Diah Junia Eksi Palupi, Martianus Frederic Ezerman

2023 Proceedings - 2023 IEEE International Conference on Cryptography, Informatics, and Cybersecurity: Cryptography and Cybersecurity: Roles, Prospects, and Challenges, ICoCICs 2023 Conference paper Cited by 1

Abstract

The linear complexity of a periodic binary sequence is the degree of its minimal polynomial. It has been conjectured that, for any positive integer n ≥ 4, there exist binary modified de Bruijn sequences of order n whose linear complexity is 2n-2, which is the highest possible. A proof remains elusive, much less a constructive general approach to such modified binary sequences, given any arbitrary order n. This work focuses on a small class of modified binary de Bruijn sequences whose linear spans are maximal or near maximal. We devise a method to determine the liner span of the sequences in this class and show heuristically that the sequences have high linear spans, often reaching the maximal values for their respective order n. © 2023 IEEE.

Affiliations

Universitas Negeri Yogyakarta, 1 Colombo Road, Department of Mathematics Education, Yogyakarta, 55281, Indonesia; Universitas Gadjah Mada, Sekip Utara Bls 21, Department of Mathematics, Yogyakarta, 55281, Indonesia; Nanyang Technological University, 21 Nanyang Link, School of Physical and Mathematical Sciences, Singapore; Sandhiguna R&d Lab, Graha Pena, Kepulauan Riau, Batam, Indonesia

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