تقرير
On the structure of $1$-generator quasi-polycyclic codes over finite chain rings
| العنوان: | On the structure of $1$-generator quasi-polycyclic codes over finite chain rings |
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| المؤلفون: | Wu, Rongsheng, Shi, Minjia, Solé, Patrick |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Information Theory |
| الوصف: | Quasi-polycyclic (QP for short) codes over a finite chain ring $R$ are a generalization of quasi-cyclic codes, and these codes can be viewed as an $R[x]$-submodule of $\mathcal{R}_m^{\ell}$, where $\mathcal{R}_m:= R[x]/\langle f\rangle$, and $f$ is a monic polynomial of degree $m$ over $R$. If $f$ factors uniquely into monic and coprime basic irreducibles, then their algebraic structure allow us to characterize the generator polynomials and the minimal generating sets of 1-generator QP codes as $R$-modules. In addition, we also determine the parity check polynomials for these codes by using the strong Gr\"{o}bner bases. In particular, via Magma system, some quaternary codes with new parameters are derived from these 1-generator QP codes. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2111.04914 |
| رقم الأكسشن: | edsarx.2111.04914 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |