A conjecture on affine planes of prime order
Journal of Combinatorial Theory Series A
A note on permutation polynomials and finite geometries
Discrete Mathematics
Affine planes and permutation polynomials
Coding theory and design theory: part II, design theory
Finite geometries
Arcs and Ovals from Abelian Groups
Designs, Codes and Cryptography
Cartesian authentication codes from functions with optimal nonlinearity
Theoretical Computer Science
APN functions in odd characteristic
Discrete Mathematics - Special issue: Combinatorics 2000
Nonlinear functions in abelian groups and relative difference sets
Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Journal of Complexity - Special issue on coding and cryptography
A family of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
Planar polynomials for commutative semifields with specified nuclei
Designs, Codes and Cryptography
Pseudo-Paley graphs and skew Hadamard difference sets from presemifields
Designs, Codes and Cryptography
Bundles, presemifields and nonlinear functions
Designs, Codes and Cryptography
Some Theorems on Planar Mappings
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
New Perfect Nonlinear Multinomials over F$_{p^{2k}}$ for Any Odd Prime p
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
A New Tool for Assurance of Perfect Nonlinearity
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases
Mathematical Methods in Computer Science
New Commutative Semifields and Their Nuclei
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the covering structures of two classes of linear codes from perfect nonlinear functions
IEEE Transactions on Information Theory
Nonlinear functions in abelian groups and relative difference sets
Discrete Applied Mathematics
New semifields, PN and APN functions
Designs, Codes and Cryptography
Proofs of two conjectures on ternary weakly regular bent functions
IEEE Transactions on Information Theory
Polarities and unitals in the Coulter---Matthews planes
Designs, Codes and Cryptography
Strongly regular graphs associated with ternary bent functions
Journal of Combinatorial Theory Series A
Switching construction of planar functions on finite fields
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
New commutative semifields defined by new PN multinomials
Cryptography and Communications
Non-Existence of isomorphisms between certain unitals
Designs, Codes and Cryptography
A character theoretic approach to planar functions
Cryptography and Communications
A theory of highly nonlinear functions
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Further results on planar DO functions and commutative semifields
Designs, Codes and Cryptography
Equivalence classes of functions between finite groups
Journal of Algebraic Combinatorics: An International Journal
A new construction of the d-dimensional Buratti-Del Fra dual hyperoval
European Journal of Combinatorics
On the number of distinct values of a class of functions over a finite field
Finite Fields and Their Applications
The weight distribution of a class of p-ary cyclic codes
Finite Fields and Their Applications
Dembowski-Ostrom polynomials from Dickson polynomials
Finite Fields and Their Applications
Perfect nonlinear binomials and their semifields
Finite Fields and Their Applications
On the dual of a Coulter--Matthews bent function
Finite Fields and Their Applications
Recent progress in algebraic design theory
Finite Fields and Their Applications
Sequences and functions derived from projective planes and their difference sets
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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Planar functions were introduced by Dembowski and Ostrom [4] to describe projective planes possessinga 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 resolvesin the negative a question posed in [4]. These planar functions define at least one such affine plane of order 3 ^efor every e ≥ 4 and their projective closures are of Lenz-Barlotti type II. All previously known planes of type IIare obtained by derivation or lifting. At least when e is odd, the planes described here cannot be obtained in thismanner.