Design theory
The solution of the Waterloo problem
Journal of Combinatorial Theory Series A
Relative difference sets with n = 2
Discrete Mathematics
A survey on relative difference sets
GDSTM '93 Proceedings of a special research quarter on Groups, difference sets, and the monster
Planar Functions and Planes of Lenz-Barlotti Class II
Designs, Codes and Cryptography
On (p^a, p^b, p^a, p^a-b)-Relative DifferenceSets
Journal of Algebraic Combinatorics: An International Journal
A unifying construction for difference sets
Journal of Combinatorial Theory Series A
New Families of Semi-Regular Relative Difference Sets
Designs, Codes and Cryptography
Difference Sets and Hyperovals
Designs, Codes and Cryptography
Almost perfect nonlinear power functions on GF (2n): the Niho case
Information and Computation
Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets
Journal of Combinatorial Theory Series A
Multiplicative Difference Sets via Additive Characters
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
European Journal of Combinatorics
Cyclic relative difference sets with classical parameters
Journal of Combinatorial Theory Series A
APN functions in odd characteristic
Discrete Mathematics - Special issue: Combinatorics 2000
New families of almost perfect nonlinear power mappings
IEEE Transactions on Information Theory
Almost perfect nonlinear power functions on GF(2n): the Welch case
IEEE Transactions on Information Theory
Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
IEEE Transactions on Information Theory
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences
Finite Fields and Their Applications
A family of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
Designs, Codes and Cryptography
Bundles, presemifields and nonlinear functions
Designs, Codes and Cryptography
A new characterization of group action-based perfect nonlinearity
Discrete Applied Mathematics
Note: APN permutations on Zn and Costas arrays
Discrete Applied Mathematics
Proofs of two conjectures on ternary weakly regular bent functions
IEEE Transactions on Information Theory
On the nonlinearity of exponential welch costas functions
IEEE Transactions on Information Theory
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During the past decade, perfect, almost perfect and maximum nonlinear functions on finite fields have been thoroughly investigated. The main tool to investigate these functions is the Walsh-Hadamard transform. This is a special version of the more general discrete Fourier transform. It is the purpose of this paper to show that the main results on nonlinear functions can be easily generalized to the case of arbitrary abelian groups if the Walsh-Hadamard transform is replaced by the discrete Fourier transform. This approach has three advantages: • Proofs become more transparent. • The connection with (relative) difference sets becomes apparent. • It yields possible generalizations to nonlinear functions on abelian groups.