تقرير
Higher weight spectra and Betti numbers of Reed-Muller codes $RM_2(2,2)$
| العنوان: | Higher weight spectra and Betti numbers of Reed-Muller codes $RM_2(2,2)$ |
|---|---|
| المؤلفون: | Ghorpade, Sudhir R., Johnsen, Trygve, Ludhani, Rati, Pratihar, Rakhi |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Computer Science - Information Theory, Primary: 94B05, 94B27, 11B65, Secondary: 14G50 |
| الوصف: | We determine the higher weight spectra of $q$-ary Reed-Muller codes $C_q=RM_q(2,2)$ for all prime powers $q$. This is equivalent to finding the usual weight distributions of all extension codes of $C_q$ over every field extension of $F_q$ of finite degree. To obtain our results we will utilize well-known connections between these weights and properties of the Stanley-Reisner rings of a series of matroids associated to each code $C_q$. In the process, we are able to explicitly determine all the graded Betti numbers of matroids associated to $C_q$ and its elongations. Comment: 44 pages, 3 appendices, 25 tables |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.02548 |
| رقم الأكسشن: | edsarx.2408.02548 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |