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Commutative semifields from projection mappings

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Abstract

We describe a general projection method to construct commutative semifields in odd characteristic. One application yields a family of commutative semifields of order q 2m with middle nucleus of order at least q 2 for every odd prime-power q and every odd integer m > 1. Another application of the method yields a generalization of the Budaghyan–Helleseth family and also greatly simplifies the construction.

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Authors and Affiliations

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

    Jürgen Bierbrauer

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  1. Jürgen Bierbrauer
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Correspondence to Jürgen Bierbrauer.

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Communicated by G. Lunardon.

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Bierbrauer, J. Commutative semifields from projection mappings. Des. Codes Cryptogr. 61, 187–196 (2011). https://doi.org/10.1007/s10623-010-9447-z

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  • DOI: https://doi.org/10.1007/s10623-010-9447-z

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