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

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 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 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 is… Expand

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, these… Expand

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

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

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