The goal of this talk is to extend the existing families of recursive coding
constructions, such as Reed-Muller codes or polar codes.  We consider m-variate
Boolean polynomials of degree r or less and evaluate them on the binary m-tuples
of a given Hamming weight b.  From the coding perspective, this setting defines
a punctured binary Reed-Muller code RM(r,m) whose positions form a Hamming
sphere of weight b in the m-dimensional  binary space.  In this talk,  we
specify some recursive properties of this single-layer spherical construction
and define its code parameters for arbitrary values  of the input  parameters m,
 r,  and b.