Hokkaido Mathematical Journal

MINAMI Kaori, NAKAGAWA Nobuo,

On planar functions of elementary abelian $p$-group type.

Hokkaido Mathematical Journal, 37 (2008) pp.531-544

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Abstract

We proved affine planes corresponding to quadratic planar functions over F_{p^n} are semifield planes, and we determined affine planes corresponding to planar functions f(x) = x^10 − αx^6 − α^2x^2 by Ding and Yuan. Moreover we calculated explicit shapes of planar functions from the square mappings of almost all known finite commutative semifields.

MSC(Primary)51E20
MSC(Secondary)
Uncontrolled Keywordsplanar function, projective plane, finite field, finite semifield, relative difference set, collineation group.