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The solution of the Waterloo problem
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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
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Cyclic relative difference sets with classical parameters
Journal of Combinatorial Theory Series A
APN functions in odd characteristic
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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
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences
Finite Fields and Their Applications
EA and CCZ Equivalence of Functions over GF(2n)
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases
Mathematical Methods in Computer Science
Switching construction of planar functions on finite fields
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Association schemes arising from bent functions
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
Cryptography and Communications
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CANS'06 Proceedings of the 5th international conference on Cryptology and Network Security
Equivalence classes of functions between finite groups
Journal of Algebraic Combinatorics: An International Journal
CCZ and EA equivalence between mappings over finite Abelian groups
Designs, Codes and Cryptography
A note on vectorial bent functions
Information Processing Letters
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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.