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Planar functions were introduced by Dembowski and Ostrom ([4]) to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a(More)
Strong conditions are derived for when two commutative presemi-fields are isotopic. It is then shown that any commutative presemifield of odd order can be described by a planar Dembowski-Ostrom polynomial and conversely , any planar Dembowski-Ostrom polynomial describes a commutative presemifield of odd order. These results allow a classification of all(More)
1 Dembowski-Ostrom Polynomials and Linearised Polynomials Let p be a prime and q = p e. Let F q denote the finite field of order q and F * q represent the set of non-zero elements of F q. The ring of polynomials in the indeterminate X with coefficients from F q will be represented by F q [X]. A polynomial f ∈ F q [X] which permutes F q under evaluation is(More)