Planar functions were introduced by Dembowski and Ostrom () 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)
This paper describes a compact, lightweight and ultra-low power ambulatory wireless EEG system based upon QUASAR's innovative noninvasive bioelectric sensor technologies. The sensors operate through hair without skin preparation or conductive gels. Mechanical isolation built into the harness permits the recording of high quality EEG data during ambulation.… (More)
Let H be a subgroup of the multiplicative group of a finite field. In this note we give a method for constructing permutation polynomials over the field using a bi-jective map from H to a coset of H. A similar, but inequivalent, method for lifting permutation behaviour of a polynomial to an extension field is also given.
Several authors have recently shown that a planar function over a finite field of order q must have at least (q + 1)/2 distinct values. In this note this result is extended by weakening the hypothesis significantly and strengthening the conclusion. We also give an algorithm for determining whether a given bivariate polynomial φ(X, Y) can be written as f (X… (More)
The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified.
Part of the Care software development system processes input les to produce code in a target language. In this paper we present the details of this code synthesis process. based on transformations of a graphical representation of the fragment collection. We include consideration of optimisation and recursion.
Motivated by several recent results, we determine precisely when F k (X d , a) − F k (0, a) is a Dembowski-Ostrom polynomial, where F k (X, a) is a Dickson polynomial of the first or second kind. As a consequence, we obtain a classification of all such polynomials which are also planar; all examples found are equivalent to previously known examples.