The weights of cubic 3-rotation symmetric Boolean functions

Rotation symmetric (RS for short) Boolean functions have been studied for about 25 years because they can be used in coding theory and cryptography. Since 2007 the k -RS functions (where k=1 gives the RS functions) for k>1 have been used for research in the same areas. The theory of the cubic k -RS functions for k=2 was developed in a 2015 paper of Cusick and Johns and for k=3 was developed in a 2015 paper of Cusick and Cheon. The 3-RS functions are divided into three forms in the latter paper, namely pure form, simple form and mixed form functions. That paper only considers the mixed form functions and mainly focuses on the affine equivalence classes for those functions. The present paper studies the (Hamming) weights of the 3-RS cubic functions for all three of the possible forms.