Abstract
In this paper, it is shown that extremal (Hermitian) self-dual codes over F 2 × F 2 exist only for lengths 1, 2, 3, 4, 5, 8 and 10. All extremal self-dual codes over F 2 × F 2 are found. In particular, it is shown that there is a unique extremal self-dual code up to equivalence for lengths 8 and 10. Optimal self-dual codes are also investigated. A classification is given for binary [12, 7, 4] codes with dual distance 4, binary [13, 7, 4] codes with dual distance 4 and binary [13, 8, 4] codes with dual distance ≥ 4.
| Original language | English |
|---|---|
| Pages (from-to) | 171-186 |
| Number of pages | 16 |
| Journal | Designs, Codes, and Cryptography |
| Volume | 28 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2003 Mar 1 |
| Externally published | Yes |
Keywords
- optimal codes
- self-dual codes
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics
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Cite this
Betsumiya, K., Gulliver, T. A., & Harada, M. (2003). Extremal self-dual codes over F 2 × F 2 Designs, Codes, and Cryptography, 28(2), 171-186. https://doi.org/10.1023/A:1022540524423