1-perfect uniform and distance invariant partitions

Let F-n be the n-dimensional vector space over Z(2). A (binary) 1-perfect p artition of F-n is a partition of F-n into (binary) perfect single error-co rrecting codes or 1-perfect codes. We define two metric properties for 1-pe rfect partitions: uniformity and distance invariance. Then we prove the equ ivalence between these properties and algebraic properties of the code (the class containing the zero vector). In this way, we characterize 1-perfect partitions obtained using 1-perfect translation invariant and not translati on invariant propelinear codes. The search for examples of 1-perfect unifor m but not distance invariant partitions enabled us to deduce a non-Abelian propelinear group structure for any Hamming code of length greater than 7.