On the metrical rigidity of binary codes

A code C in the n-dimensional vector space En over GF(2) is called metrically rigid if every isometry I: C → En with respect to the Hamming metric is extendable to an isometry of the whole space En. A code C is reduced if it contains the all-zero vector. For n large enough the metrical rigidity of length n reduced binary codes containing a 2-(n,k,λ)-design is proved. The class of such codes includes all the families of uniformly packed codes of sufficiently large length satisfying the condition d-ρ ≥ 2, where d is the code distance and ρ is the covering radius.