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Towards the classification of rank 2 semifields 6-dimensional over their center

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Abstract

Semifields 6-dimensional over the center \({\mathbb F_q}\), having at least one nucleus of order q 3 and at least one of the remaining nuclei of order q 2, are partitioned into non-empty mutually non-isotopic classes. Also, for each class a canonical form for the multiplication is presented.

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Authors and Affiliations

  1. Dipartimento di Matematica, Seconda Università degli Studi di Napoli, 81100, Caserta, Italy

    Giuseppe Marino & Olga Polverino

  2. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, 80126, Napoli, Italy

    Rocco Trombetti

Authors
  1. Giuseppe Marino
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  2. Olga Polverino
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  3. Rocco Trombetti
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Corresponding author

Correspondence to Olga Polverino.

Additional information

Communicated by Simeon Ball.

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Marino, G., Polverino, O. & Trombetti, R. Towards the classification of rank 2 semifields 6-dimensional over their center. Des. Codes Cryptogr. 61, 11–29 (2011). https://doi.org/10.1007/s10623-010-9436-2

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  • DOI: https://doi.org/10.1007/s10623-010-9436-2

Keywords

Mathematics Subject Classification (2000)