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A new almost perfect nonlinear function which is not quadratic
It is shown that the approach shown can be used to construct a ''non-quadratic'' APN function, which is in remarkable contrast to all recently constructed functions which have all been quadratic. Expand
Finite Geometry and Character Theory
Preliminaries: Incidence structures with singer groups.- Examples: Existence and non-existence.- Difference sets with classical parameters.- Semiregular relative difference sets.- Projective planesExpand
Perfect and Almost Perfect Sequences
This paper focuses on the existence problem for perfect and almost perfect binary periodic sequences; such sequences are actually equivalent to certain cyclic difference sets and cyclic divisible difference sets, respectively, structures which have been studied in Design Theory for a long time. Expand
New classes of almost bent and almost perfect nonlinear polynomials
New infinite classes of almost bent and almost perfect nonlinear polynomials are constructed. It is shown that they are affine inequivalent to any sum of a power function and an affine function
A new APN function which is not equivalent to a power mapping
A new almost-perfect nonlinear function (APN) on F(2/sup 10/) which is not equivalent to any of the previously known APN mappings is constructed. This is the first example of an APN mapping which isExpand
A new family of semifields with 2 parameters
Abstract A new family of commutative semifields with two parameters is presented. Its left and middle nucleus are both determined. Furthermore, we prove that for different pairs of parameters, theseExpand
On Boolean Functions Which Are Bent and Negabent
This paper considers functions f which are simultaneously bent and negabent, i.e. which have optimum periodic and negaperiodic properties and several constructions and classifications are presented. Expand
APN functions in odd characteristic
The notion of ''APN'' has been extended to the nonbinary case and several such mappings have been discovered and some more examples are added. Expand
On the Maximum Number of Bent Components of Vectorial Functions
The binomials of the maximum number of bent component functions of a vectorial function is shown to be F:GF(2)^{n}-2^{n/2}$ and the functions have differential properties much better than those of the only known power functions. Expand
Existence and nonexistence of almost-perfect autocorrelation sequences
The authors apply known theorems on divisible difference sets to simplify and strengthen results by J. Wolfmann and answer two questions which were posed by Wolfman. Expand