Matrix-Valued Binary Bent Functions

In theory and practice of bent functions, the term class is used in a twofold meaning. Most often, it is applied to sets of bent functions generated in a specified manner or by a particular algorithm. In this respect, several classes of bent functions are distinguished [1–3]. In another meaning, the term classes refers to sets of bent functions sharing certain specific properties or are mutually related by some transformations. For example, already Rothaus proved that for $$n=6$$ there are four classes of bent functions that are affine equivalent, i.e., functions from the same class can be converted to each other by affine transformations [4]. Table 6.1 shows representative functions for these classes [4].