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.
翻译：我们确定某些特殊贝贝利族群体代码的最小含水重量条件,因此,我们确定,任何此类代码,最多为变异等值,对于某些合适的正正数整数美元和美元,其次空间为长度重复代码美元副本的美元数,对于某些合适的正数整数美元和美元数。此外,我们提供了线性代码 $C ⁇ bigoplop ⁇ i=1 ⁇ s}Rep ⁇ t}(\mathb{F ⁇ q}) 美元(mathb{F ⁇ q}) 美元数的整数的完整特性,我们确定,对于每对整数美元,t\geq1美元,这种代码是一种贝利族群体代码。最后,我们以与亚贝利族群体代码类似的方式,对环形群代码作了相同的特性说明。
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