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Fractional Jumps: Complete Characterisation and an Explicit Infinite Family

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Arithmetic of Finite Fields (WAIFI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11321))

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Abstract

In this paper we provide a complete characterisation of transitive fractional jumps. In particular, we prove that they can only arise from transitive projective automorphisms apart from a couple of degenerate cases which we entirely classify. Furthermore, we prove that such construction is feasible for arbitrarily large dimension by exhibiting an infinite class of projectively primitive polynomials whose companion matrix can be used to define a full orbit sequence over an affine space.

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Acknowledgment

The authors are grateful to Andrea Ferraguti for preliminary reading of this manuscript, and for useful discussions and suggestions. The second author is thankful to the Swiss National Science Foundation grant number 171248.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, UK

    Federico Amadio Guidi & Giacomo Micheli

Authors
  1. Federico Amadio Guidi
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  2. Giacomo Micheli
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Corresponding author

Correspondence to Giacomo Micheli .

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Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Lilya Budaghyan

  2. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Mexico, Mexico

    Francisco Rodríguez-Henríquez

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Amadio Guidi, F., Micheli, G. (2018). Fractional Jumps: Complete Characterisation and an Explicit Infinite Family. In: Budaghyan, L., Rodríguez-Henríquez, F. (eds) Arithmetic of Finite Fields. WAIFI 2018. Lecture Notes in Computer Science(), vol 11321. Springer, Cham. https://doi.org/10.1007/978-3-030-05153-2_14

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  • DOI: https://doi.org/10.1007/978-3-030-05153-2_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05152-5

  • Online ISBN: 978-3-030-05153-2

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