On metric rigidity for some classes of codes

A code $C$ in the $n$-dimensional metric space $\mathbb F^n_q$ over the Galois field $GF(q)$ is said to be metrically rigid if any isometry $I\colon C\to\mathbb F^n_q$ can be extended to an isometry (automorphism) of $\mathbb F^n_q$. We prove metric rigidity for some classes of codes, including certain classes of equidistant codes and codes corresponding to one class of affine resolvable designs.