On metric rigidity for some classes of codes

Abstract

A code C in the n-dimensional metric space $$ \mathbb{F}_q^n $$ over the Galois field GF(q) is said to be metrically rigid if any isometry I: C ? $$ \mathbb{F}_q^n $$ can be extended to an isometry (automorphism) of $$ \mathbb{F}_q^n $$ . 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.