Geodesic
On isotopisms and strong isotopisms of commutative presemifields
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 247-261.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we prove that the $P(q,\ell )$ (q odd prime power and $\ell >1$ odd) commutative semifields constructed by Bierbrauer (Des. Codes Cryptogr. 61:187-196, 2011) are isotopic to some commutative presemifields constructed by Budaghyan and Helleseth (SETA, pp. 403-414, 2008). 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.
Keywords: commutative semifields, symplectic semifields, isotopy, strong isotopy, planar DO polynomials 
@article{JAC_2012__36_2_a3,
     author = {Marino, G. and Polverino, O.},
     title = {On isotopisms and strong isotopisms of commutative presemifields},
     journal = {Journal of Algebraic Combinatorics},
     pages = {247--261},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a3/}
}
TY  - JOUR
AU  - Marino, G.
AU  - Polverino, O.
TI  - On isotopisms and strong isotopisms of commutative presemifields
JO  - Journal of Algebraic Combinatorics
PY  - 2012
SP  - 247
EP  - 261
VL  - 36
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a3/
LA  - en
ID  - JAC_2012__36_2_a3
ER  - 
%0 Journal Article
%A Marino, G.
%A Polverino, O.
%T On isotopisms and strong isotopisms of commutative presemifields
%J Journal of Algebraic Combinatorics
%D 2012
%P 247-261
%V 36
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a3/
%G en
%F JAC_2012__36_2_a3
Marino, G.; Polverino, O. On isotopisms and strong isotopisms of commutative presemifields. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 247-261. http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a3/