Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2008
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| _version_ | 1866914278176456704 |
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| author | Abdukhalikov, Kanat Bannai, Eiichi Suda, Sho |
| author_facet | Abdukhalikov, Kanat Bannai, Eiichi Suda, Sho |
| contents | H. Cohn et. al. proposed an association scheme of 64 points in R^{14} which is conjectured to be a universally optimal code. We show that this scheme has a generalization in terms of Kerdock codes, as well as in terms of maximal real mutually unbiased bases. These schemes also related to extremal line-sets in Euclidean spaces and Barnes-Wall lattices. D. de Caen and E. R. van Dam constructed two infinite series of formally dual 3-class association schemes. We explain this formal duality by constructing two dual abelian schemes related to quaternary linear Kerdock and Preparata codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0802_1425 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets Abdukhalikov, Kanat Bannai, Eiichi Suda, Sho Combinatorics General Mathematics 05E30, 94B60, 51M15, 11H06 H. Cohn et. al. proposed an association scheme of 64 points in R^{14} which is conjectured to be a universally optimal code. We show that this scheme has a generalization in terms of Kerdock codes, as well as in terms of maximal real mutually unbiased bases. These schemes also related to extremal line-sets in Euclidean spaces and Barnes-Wall lattices. D. de Caen and E. R. van Dam constructed two infinite series of formally dual 3-class association schemes. We explain this formal duality by constructing two dual abelian schemes related to quaternary linear Kerdock and Preparata codes. |
| title | Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets |
| topic | Combinatorics General Mathematics 05E30, 94B60, 51M15, 11H06 |
| url | https://arxiv.org/abs/0802.1425 |