Designs, Codes and Cryptography

, Volume 33, Issue 1, pp 39–43

A Proof of Simmons' Conjecture

  • Tor Helleseth
  • Johannes Mykkeltveit

DOI: 10.1023/B:DESI.0000032605.98142.7f

Cite this article as:
Helleseth, T. & Mykkeltveit, J. Designs, Codes and Cryptography (2004) 33: 39. doi:10.1023/B:DESI.0000032605.98142.7f


An open problem posed by Simmons is whether two given permutations of the vertices of the deBruijn graph have the same cycle structure, or not. We present a solution to this problem and find the complete cycle structure.

deBruijn graph sequences nonlinear shiftregisters 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Tor Helleseth
    • 1
  • Johannes Mykkeltveit
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Rogaland ResearchBergenNorway