  We determine a condition on the minimum Hamming weight of some special
abelian group codes and, as a consequence of this result, we establish that any
such code is, up to permutational equivalence, a subspace of the direct sum of
$s$ copies of the repetition code of length $t$, for some suitable positive
integers $s$ and $t$. Moreover, we provide a complete characterisation of
permutation automorphisms of the linear code
$C=\bigoplus_{i=1}^{s}Rep_{t}(\mathbb{F}_{q})$ and we establish that such a
code is an abelian group code, for every pair of integers $s,t\geq1$. Finally,
in a similar fashion as for abelian group codes, we give an equivalent
characterisation of cyclic group codes.
