Linear symmetries of Boolean functions Original Research Article

In this note we study the linear symmetry group image of a Boolean function f of n variables, that is, the set of all image which leave f invariant, where image is the general linear group on the field of two elements. The main problem is that of concrete representation: which subgroups G of image can be represented as image for some n-ary k-valued Boolean function f. We call such subgroups linearly representable. The main results of the note may be summarized as follows: