Self-dual Codes over the Kleinian Four Group
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2000
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| _version_ | 1866909834209656832 |
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| author | Höhn, Gerald |
| author_facet | Höhn, Gerald |
| contents | We introduce self-dual codes over the Kleinian four group $K = \mathbb{Z}_2 \times \mathbb{Z}_2$ for a natural quadratic form on $K^n$ and develop the theory. Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes. Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices and vertex operator algebras. This analogy will be emphasized and explained in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0005266 |
| institution | arXiv |
| publishDate | 2000 |
| record_format | arxiv |
| spellingShingle | Self-dual Codes over the Kleinian Four Group Höhn, Gerald Combinatorics Group Theory Number Theory Quantum Algebra We introduce self-dual codes over the Kleinian four group $K = \mathbb{Z}_2 \times \mathbb{Z}_2$ for a natural quadratic form on $K^n$ and develop the theory. Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes. Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices and vertex operator algebras. This analogy will be emphasized and explained in detail. |
| title | Self-dual Codes over the Kleinian Four Group |
| topic | Combinatorics Group Theory Number Theory Quantum Algebra |
| url | https://arxiv.org/abs/math/0005266 |