Symmetric 2$-$(36,15,6) designs with an automorphism of order two
| Autor: | Rukavina, Sanja, Tonchev, Vladimir D. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 |
| Databáze: | arXiv |
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