On Jackson's theorem in the space $\ell_2(\mathbb Z_2^n)$

Estimates of Jackson's constants in the space v are given for the case of approximation by sums of subspaces on which irreducible representations of the isometry group of $\mathbb Z_2^n$ act and for the case in which the modulus of continuity is defined using generalized translations. Coding theory results on efficiency estimates for binary $d$-codes with respect to the Hamming distance are used.