The generalized automorphisms of Reed-Muller code and McEliece–Sidelnikov public key cryptosystem

The McEliece–Sidelnikov public key cryptosystem is the modification of the McEliece public key cryptosystem using $u$-fold Reed–Muller code. In the work, we investigate the structure of public key sets of the cryptosystem in the case of any number of blocks $u$. In case $u=2$, the equivalence classes of private keys with representatives of a special kind are described.