Bounds for the multicovering radii of Reed-Muller codes with applications to stream ciphers

The multicovering radii of a code are recent generalizations of the coverin g radius of a code. For positive m, the m-covering radius of C is the least radius t such that every m-tuple of vectors is contained in at least one b all of radius t centered at some codeword. In this paper upper bounds are f ound for the multicovering radii of first order Reed-Muller codes. These bo unds generalize the well-known Norse bounds for the classical covering radi i of first order Reed-Muller codes. They are exact in some cases. These bou nds are then used to prove the existence of secure families of keystreams a gainst a general class of cryptanalytic attacks. This solves the open quest ion that gave rise to the study of multicovering radii of codes.