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- Robert S. Coulter, Rex W. Matthews
- Des. Codes Cryptography
- 1997

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 aâ€¦ (More)

, where Ï‡ is a non-trivial additive character of Fq and f âˆˆ Fq[X ]. In this article we consider the evaluation of all Weil sums where f(X) = aX +1 +L(X) and p = 2. Here, a âˆˆ Fq, Î± is any naturalâ€¦ (More)

where f âˆˆ Fq[X ]. These sums are also known as Weil sums. The problem of explicitly evaluating these sums is quite often difficult. Results giving estimates for the absolute value of the sum are moreâ€¦ (More)

Strong conditions are derived for when two commutative presemifields are isotopic. It is then shown that any commutative presemifield of odd order can be described by a planar Dembowski-Ostromâ€¦ (More)

Let Fq denote the finite field with q = p e elements and P(Fq ) be the n-dimensional projective space over Fq . For any f âˆˆ Fq [X1, . . . , Xn] of degree d, define the homogenous polynomial f âˆ— âˆˆâ€¦ (More)

where Fq denotes the finite field of q elements (q = p e for p a prime) and f âˆˆ Fq[X]. In a recent article [2] the author gave explicit evaluations of all Weil sums with f(X) = aX Î±+1 and p odd.â€¦ (More)

- Robert S. Coulter, Marie Henderson, Rex W. Matthews
- Finite Fields and Their Applications
- 2009

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 bijective map from H to a coset of H.â€¦ (More)

Abstract. The definition of bent is redefined for any finite field. Our main result is a complete description of the relationship between bent polynomials and perfect non-linear functions over finiteâ€¦ (More)

- Robert S. Coulter, Marie Henderson
- Discrete Mathematics
- 1999

We give an alternative proof of the fact that a planar function cannot exist on groups of even order. The argument involved leads us to define a class of functions which we call semi-planar. Throughâ€¦ (More)

- Robert S. Coulter, Pamela Kosick
- Finite Fields and Their Applications
- 2014

Let q be a prime power and fix a âˆˆ Fq2 \ Fq. In this note it is proved that, provided q > 5, the set Sa = {aâˆ’ Î± : Î± âˆˆ Fq} contains both a square and a non-square of Fq2 . In particular, every a âˆˆ Fq2â€¦ (More)