On abelian and cyclic group codes
| Autor: | Marotta, Angelo |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages |
| Databáze: | arXiv |
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