Design theory
An exponent bound on skew Hadamard abelian difference sets
Designs, Codes and Cryptography
Finite fields
Planar Functions and Planes of Lenz-Barlotti Class II
Designs, Codes and Cryptography
Skew-Hadamard Matrices and the Smith Normal Form
Designs, Codes and Cryptography
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
Constructions of External Difference Families and Disjoint Difference Families
Designs, Codes and Cryptography
Skew Hadamard difference sets from the Ree--Tits slice symplectic spreads in PG(3,32h+1)
Journal of Combinatorial Theory Series A
Efficient matrix rank computation with application to the study of strongly regular graphs
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Pseudo-Paley graphs and skew Hadamard difference sets from presemifields
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Codebooks from almost difference sets
Designs, Codes and Cryptography
Some Theorems on Planar Mappings
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
A Class of Nonbinary Codes and Sequence Families
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
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
Some results on skew Hadamard difference sets
Designs, Codes and Cryptography
A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases
Mathematical Methods in Computer Science
Special subsets of difference sets with particular emphasis on skew Hadamard difference sets
Designs, Codes and Cryptography
Properties and applications of preimage distributions of perfect nonlinear functions
IEEE Transactions on Information Theory
On the covering structures of two classes of linear codes from perfect nonlinear functions
IEEE Transactions on Information Theory
Non-abelian skew Hadamard difference sets fixed by a prescribed automorphism
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
Cyclotomic constructions of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
A character theoretic approach to planar functions
Cryptography and Communications
A note of perfect nonlinear functions
CANS'06 Proceedings of the 5th international conference on Cryptology and Network Security
Further results on planar DO functions and commutative semifields
Designs, Codes and Cryptography
Difference sets and doubly transitive actions on Hadamard matrices
Journal of Combinatorial Theory Series A
On the number of distinct values of a class of functions over a finite field
Finite Fields and Their Applications
More explicit classes of permutation polynomials of F33m
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
Sequences and functions derived from projective planes and their difference sets
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
On the relationships between perfect nonlinear functions and universal hash families
Theoretical Computer Science
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In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics.