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Cryptography and Communications

, Volume 10, Issue 6, pp 1183–1202 | Cite as

The cycle structure of LFSR with arbitrary characteristic polynomial over finite fields

  • Zuling Chang
  • Martianus Frederic Ezerman
  • San Ling
  • Huaxiong Wang
Article
Part of the following topical collections:
  1. Special Issue on Sequences and Their Applications

Abstract

We determine the cycle structure of linear feedback shift register with arbitrary monic characteristic polynomial over any finite field. For each cycle, a method to find a state and a new way to represent the state are proposed.

Keywords

Cycle structure Cyclotomic number de Bruijn sequence Decimation LFSR Periodic sequence 

Mathematics Subject Classification (2010)

11B50 94A55 94A60 

Notes

Acknowledgements

The work of Z. Chang is supported by the Joint Fund of the National Natural Science Foundation of China under Grants 61772476 and U1304604. Research Grants TL-9014101684-01 and MOE2013-T2-1-041 support the research carried out by M. F. Ezerman, S. Ling, and H. Wang.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouChina
  2. 2.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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