To Metric Rigidity of Binary Codes

A code $C$ in the $n$-dimensional metric space $E^n$ over $GF(2)$ is called metrically rigid if each isometry $I\colon C\to E^n$ can be extended to an isometry of the whole space $E^n$. For $n$ large enough, metrical rigidity of any length-$n$ binary code that contains a $2-(n,k,\lambda)$–design is proved. The class of such codes includes, for instance, all families of uniformly packed codes of large enough lengths that satisfy the condition $d-\rho\geq 2$, where $d$ is the code distance and $\rho$ is the covering radius.