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  • On the Hughes-Kleinfeld and Knuth's semifields two-dimensional over a weak nucleus
    Ball, Simeon ; Lavrauw, Michel
    In 1960 Hughes and Kleinfeld (Am J Math 82:389–392, 1960) constructed a finite semifield which is two-dimensional over a weak nucleus, given an automorphism σ of a finite field K and elements µ, η ∈ ... K with the property that xσ+1 + µx − η has no roots in K. In 1965 Knuth (J Algebra 2:182–217, 1965) constructed a further three finite semifields which are also two-dimensional over a weak nucleus, given the same parameter set (K, σ, µ, η). Moreover, in the same article, Knuth describes operations that allow one to obtain up to six semifields from a given semifield. We show how these operations in fact relate these four finite semifields, for a fixed parameter set, and yield at most five non-isotopic semifields out of a possible 24. These five semifields form two sets of semifields, one of which consists of at most two non-isotopic semifields related by Knuth operations and the other of which consists of at most three non-isotopic semifields.
    Vir: Designs, codes and cryptography. - ISSN 0925-1022 (Vol. 44, iss. 1-3, 2007, str. 63–67)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2007
    Jezik - angleški
    COBISS.SI-ID - 143112195

    Povezava(-e):

    https://link.springer.com/article/10.1007/s10623-007-9061-x
    https://doi.org/10.1007/s10623-007-9061-x
    DOI

vir: Designs, codes and cryptography. - ISSN 0925-1022 (Vol. 44, iss. 1-3, 2007, str. 63–67)

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