Multi de Bruijn Sequences and the Cross-Join Method

Abbas Alhakim and Janusz Szmidt ()
Additional contact information
Abbas Alhakim: Department of Mathematics, American University of Beirut, Beirut 11072020, Lebanon
Janusz Szmidt: Department of Cryptology, Military Communication Institute, ul.Warszawska 22A, 05-130 Zegrze Poludniowe, Poland

Mathematics, 2023, vol. 11, issue 5, 1-9

Abstract: We show a method to construct binary multi de Bruijn sequences using the cross-join method. We extend the proof given by Alhakim for ordinary de Bruijn sequences to the case of multi de Bruijn sequences. In particular, we establish that all multi de Bruijn sequences can be obtained by cross-joining an ordinary de Bruijn sequence concatenated with itself an appropriate number of times. We implemented the generation of all multi de Bruijn sequences of type C ( 2 , 2 , 2 ) and C ( 3 , 2 , 2 ) . We experimentally confirm that some multi de Bruijn sequences can be generated by Galois Nonlinear Feedback Shift Registers (NLFSRs). It is supposed that all multi de Bruijn sequences can be generated using Galois NLFSRs.

Keywords: multi de Bruijn sequences; cross-join method; Galois NLFSRs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/5/1262/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/5/1262/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:5:p:1262-:d:1088743

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().