تقرير
On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes
| العنوان: | On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes |
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| المؤلفون: | Ghorpade, Sudhir R., Ludhani, Rati |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra, Computer Science - Information Theory, 13D02, 94B05 |
| الوصف: | Following Johnsen and Verdure (2013), we can associate to any linear code $C$ an abstract simplicial complex and in turn, a Stanley-Reisner ring $R_C$. The ring $R_C$ is a standard graded algebra over a field and its projective dimension is precisely the dimension of $C$. Thus $R_C$ admits a graded minimal free resolution and the resulting graded Betti numbers are known to determine the generalized Hamming weights of $C$. The question of purity of the minimal free resolution of $R_C$ was considered by Ghorpade and Singh (2020) when $C$ is the generalized Reed-Muller code. They showed that the resolution is pure in some cases and it is not pure in many other cases. Here we give a complete characterization of the purity of graded minimal free resolutions of Stanley-Reisner rings associated to generalized Reed-Muller codes of an arbitrary order. Comment: 8 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2102.00308 |
| رقم الأكسشن: | edsarx.2102.00308 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |