Abstract
Symmetric designs and Hadamard matrices are used to construct binary and ternary self-dual codes. Orthogonal designs are shown to be useful in construction of self-dual codes over large fields. In this paper, we first introduce a new array of order 12, which is suitable for any set of four amicable circulant matrices. We apply some orthogonal designs of order 12 to construct new self-dual codes over large finite fields, which lead us to the odd Leech lattice by Construction A.
| Original language | English |
|---|---|
| Pages (from-to) | 184-194 |
| Number of pages | 11 |
| Journal | Journal of Combinatorial Designs |
| Volume | 13 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2005 Dec 1 |
| Externally published | Yes |
Keywords
- Orthogonal design
- Self-dual code
- The Leech lattice
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
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Cite this
Harada, M., & Kharaghani, H. (2005). Orthogonal designs, self-dual codes, and the Leech lattice. Journal of Combinatorial Designs, 13(3), 184-194. https://doi.org/10.1002/jcd.20046