2019-08-15
Uniqueness of codes using semidefinite programming
Publication
Publication
Designs, Codes and Cryptography , Volume 87 p. 1881- 1895
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.
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| doi.org/10.1007/s10623-018-0589-8 | |
| Designs, Codes and Cryptography | |
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Brouwer, A., & Polak, S. (2019). Uniqueness of codes using semidefinite programming. Designs, Codes and Cryptography, 87, 1881–1895. doi:10.1007/s10623-018-0589-8 |
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