A constant-weight code is an error-correcting code in which every codeword has the same Hamming
weight. For binary codes, this means that each codeword
contains the same number 
of ones. Let 
be the greatest number of binary codewords
of length 
,
weight 
,
and pairwise Hamming distance at least 
(Dzoba 2026).
Dzoba (2026) constructed codes giving the following improved lower bounds. These are existence bounds, not claims of optimality.
 |  | lower bound for  |
| 27 | 11 | 19305 |
| 27 | 12 | 24804 |
| 27 | 13 | 27783 |
| 28 | 9 | 11388 |
| 28 | 10 | 19110 |
| 29 | 9 | 14781 |
| 29 | 10 | 27183 |
| 29 | 11 | 42042 |
Each code is a union of orbits of a prescribed permutation group. Dzoba (2026) reports that Claude designed and ran the searches and produced the constructions under the author's direction. Claude and Codex supplied separately written checking programs.
