On isotopisms and strong isotopisms of commutative presemifields

Details On isotopisms and strong isotopisms of commutative presemifields On isotopisms and strong isotopisms of commutative presemifields

2011-05-30

arxiv.org/abs/1105.5940v2

Mathematics

Combinatorics

References updated, pag. 5 corrected Multiplication of commutative LMPTB semifields

Scientific paper

In this paper we prove that the $P(q,\ell)$ ($q$ odd prime power and $\ell>1$ odd) commutative semifields constructed by Bierbrauer in \cite{BierbrauerSub} are isotopic to some commutative presemifields constructed by Budaghyan and Helleseth in \cite{BuHe2008}. Also, we show that they are strongly isotopic if and only if $q\equiv 1(mod\,4)$. Consequently, for each $q\equiv -1(mod\,4)$ there exist isotopic commutative presemifields of order $q^{2\ell}$ ($\ell>1$ odd) defining CCZ--inequivalent planar DO polynomials.

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