论文标题
在Abelian和循环组代码上
On abelian and cyclic group codes
论文作者
论文摘要
我们确定了一些特殊的Abelian组代码的最小锤量重量的条件，并且由于此结果，我们确定任何此类代码都符合排位率的等效性，即直接总和$ s $ s $ copies of Length $ t $的$ s $副本，对于某些合适的正整数$ s $ s $ s $ s $ s $和$ t $。此外，我们提供了线性代码的置换自动形态的完整表征，$ c = \ bigoplus_ {i = 1}^{s} rep_ rep_ {t}（\ Mathbb {f} _ {q}）$，我们确定了这样的代码是每个Abelian组代码，对于每个Integers $ s $ S，T \ s t c。最后，以与阿贝尔组代码相似的方式，我们给出了循环组代码的等效表征。
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.
