3 research outputs found
When a Boolean Function can be Expressed as the Sum of two Bent Functions
In this paper we study the problem that when a Boolean function can
be represented as the sum of two bent functions. This problem was
recently presented by N. Tokareva in studying the number of bent
functions. Firstly, many functions, such as
quadratic Boolean functions, Maiorana-MacFarland bent functions,
partial spread functions etc, are proved to be able to be
represented as the sum of two bent functions. Methods to construct
such functions from low dimension ones are also introduced. N.
Tokareva\u27s main hypothesis is proved for . Moreover,
two hypotheses which are equivalent to N. Tokareva\u27s main hypothesis
are presented. These hypotheses may lead to new ideas or methods to
solve this problem. At last, necessary and sufficient conditions on
the problem when the sum of several bent functions is again a bent
function are given