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A family of semifields in odd characteristic

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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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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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Correspondence to Jürgen Bierbrauer.

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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).

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