تقرير
On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups
| العنوان: | On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups |
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| المؤلفون: | Farrán, J. I., García-Sánchez, P. A., Heredia, B. A. |
| سنة النشر: | 2017 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Information Theory, Mathematics - Combinatorics, 11T71, 20M14, 11Y55 |
| الوصف: | We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, we compute the second Feng-Rao number, and provide some examples and comparisons with previous results on this topic. These calculations rely on Ap\'{e}ry sets, and thus several results concerning Ap\'ery sets of Arf semigroups are presented. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1702.08225 |
| رقم الأكسشن: | edsarx.1702.08225 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |