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A family of semifields in odd characteristic

Designs, Codes and Cryptography volume 86, pages 611–621 (2018)Cite this article

Abstract

We study a large family of semifields in odd characteristic, which contains the commutative Budaghyan–Helleseth semifields as well as semifields which are not isotopic to commutative semifields. Using a large group of autotopisms we obtain a complete classification result in certain parametric subcases.

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Acknowledgements

The research of D. Bartoli, G. Faina, S. Marcugini, and F. Pambianco was supported in part by Ministry for Education, University and Research of Italy (MIUR) (Project PRIN 2012 ”Geometrie di Galois e strutture di incidenza”) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). J. Bierbrauer’s research was supported in part by GNSAGA - INdAM.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Jürgen Bierbrauer

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, 06123, Perugia, Italy

    Daniele Bartoli, Giorgio Faina, Stefano Marcugini & Fernanda Pambianco

Authors
  1. Jürgen Bierbrauer
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  2. Daniele Bartoli
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  3. Giorgio Faina
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  4. Stefano Marcugini
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  5. Fernanda Pambianco
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Corresponding author

Correspondence to Jürgen Bierbrauer.

Additional information

Communicated by M. Lavrauw.

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Bierbrauer, J., Bartoli, D., Faina, G. et al. A family of semifields in odd characteristic. Des. Codes Cryptogr. 86, 611–621 (2018). https://doi.org/10.1007/s10623-017-0345-5

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  • DOI: https://doi.org/10.1007/s10623-017-0345-5

Keywords

  • Semifields
  • Knuth semifields
  • Isotopy
  • Budaghyan–Helleseth semifields
  • Projective polynomials
  • Nuclei

Mathematics Subject Classification

  • 12K10
  • 51E15
  • 51A40

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