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Acta Mathematica Vietnamica

, Volume 41, Issue 1, pp 171–181 | Cite as

Linear Difference Equations and Periodic Sequences over Finite Fields

  • Dang Vu GiangEmail author
Article
  • 79 Downloads

Abstract

First, we study linear equations over finite fields in general. An explicit formula for a common period is found for every solution of a linear difference equation over a finite field. It will help to estimate the p-adic modulus of polynomial roots. Second, we focus our attention on periodic sequences over finite fields and Hamiltonian cycles in de Bruijn directed graph.

Keywords

Jordan multiplicative decomposition Characteristic equations Lucas’ congruence Minimal polynomial Trace representation Max-sequences 

Mathematics Subject Classification (2010)

12E20 12Y05 

Notes

Acknowledgments

The author would like to express his sincere thank to the referee for reading carefully the manuscript and providing some suggestions that have been implemented in the final version of the paper. Deepest appreciation is extended towards the NAFOSTED (the National Foundation for Science and Technology Development in Vietnam) for the financial support.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Hanoi Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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