On Jackson's theorem in the space ℓ2(ℤ 2 n )

Estimates of Jackson's constants in the space ℓ₂(ℤ ₂ ⁿ ) are given for the case of approximation by sums of subspaces on which irreducible representations of the isometry group of (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 binaryd-codes with respect to the Hamming distance are used. Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 390–405, September, 1996.