تقرير
Symmetric 2$-$(36,15,6) designs with an automorphism of order two
| العنوان: | Symmetric 2$-$(36,15,6) designs with an automorphism of order two |
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| المؤلفون: | Rukavina, Sanja, Tonchev, Vladimir D. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05B05, 94B05 |
| الوصف: | The parameters 2-(36,15,6) are the smallest parameters of symmetric designs for which a complete classification up to isomorphism is yet unknown. Bouyukliev, Fack and Winne classified all 2-$(36,15,6)$ designs that admit an automorphism of odd prime order, and gave a partial classification of such designs that admit an automorphism of order 2. In this paper, we give the classification of all symmetric 2-$(36,15,6)$ designs that admit an automorphism of order two. It is shown that there are exactly $1 547 701$ nonisomorphic such designs, $135 779$ of which are self-dual designs. The ternary linear codes spanned by the incidence matrices of these designs are computed. Among these codes, there are near-extremal self-dual codes with previously unknown weight distributions. Comment: 20 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.03381 |
| رقم الأكسشن: | edsarx.2403.03381 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |