| Autor: |
Tabue, A. Fotue, Martínez-Moro, E., Mouaha, C. |
| Rok vydání: |
2016 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Given $\texttt{S}|\texttt{R}$ a finite Galois extension of finite chain rings and $\mathcal{B}$ an $\texttt{S}$-linear code we define two Galois operators, the closure operator and the interior operator. We proof that a linear code is Galois invariant if and only if the row standard form of its generator matrix has all entries in the fixed ring by the Galois group and show a Galois correspondence in the class of $\texttt{S}$-linear codes. As applications some improvements of upper and lower bounds for the rank of the restriction and trace code are given and some applications to $\texttt{S}$-linear cyclic codes are shown. |
| Databáze: |
arXiv |
| Externí odkaz: |
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