Abstract
For n, d, w ∈ N, let A(n, d, w) denote the maximum size of a binary code of word length n,
minimum distance d and constant weight w. Schrijver recently showed using semidefinite
programming that A(23, 8, 11) = 1288, and the second author that A(22, 8, 11) = 672
and A(22, 8, 10) = 616. Here we show uniqueness of the codes achieving these bounds.
Let A(n, d) denote the maximum size of a binary code of word length n and minimum
distance d. Gijswijt et al. showed that A(20, 8) = 256. We show that there are several
nonisomorphic codes achieving this bound, and classify all such codes with all distances
divisible by 4.
minimum distance d and constant weight w. Schrijver recently showed using semidefinite
programming that A(23, 8, 11) = 1288, and the second author that A(22, 8, 11) = 672
and A(22, 8, 10) = 616. Here we show uniqueness of the codes achieving these bounds.
Let A(n, d) denote the maximum size of a binary code of word length n and minimum
distance d. Gijswijt et al. showed that A(20, 8) = 256. We show that there are several
nonisomorphic codes achieving this bound, and classify all such codes with all distances
divisible by 4.
| Original language | English |
|---|---|
| Article number | 8 |
| Pages (from-to) | 1881-1895 |
| Number of pages | 15 |
| Journal | Designs Codes and Cryptography |
| Volume | 87 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2019 |
| Externally published | Yes |
Keywords
- Code
- Binary code
- Uniqueness
- semidefinite programming
- golay