On the metrical rigidity of binary codes

Abstract A code C in the n -dimensional vector space E n over GF (2) is called metrically rigid if every isometry I : C → E n with respect to the Hamming metric is extendable to an isometry of the whole space E n . 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.