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Linear Difference Equations and Periodic Sequences over Finite Fields

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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.

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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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Authors and Affiliations

  1. Hanoi Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam

    Dang Vu Giang

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  1. Dang Vu Giang
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Correspondence to Dang Vu Giang.

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Giang, D.V. Linear Difference Equations and Periodic Sequences over Finite Fields. Acta Math Vietnam 41, 171–181 (2016). https://doi.org/10.1007/s40306-014-0108-6

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  • DOI: https://doi.org/10.1007/s40306-014-0108-6

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