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Multi de Bruijn Sequences and the Cross-Join Method

Author

Listed:
  • 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)

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.

Suggested Citation

  • Abbas Alhakim & Janusz Szmidt, 2023. "Multi de Bruijn Sequences and the Cross-Join Method," Mathematics, MDPI, vol. 11(5), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1262-:d:1088743
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