Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00174 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915824271360000 |
|---|---|
| author | Rosin, Christopher D. |
| author_facet | Rosin, Christopher D. |
| contents | A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code with parameters $n,d,w$. We establish improved lower bounds on $A(n,d,w)$ by constructing new larger codes, for 24 values of $(n,d,w)$ with $6 \leq d \leq 18$ and $18 \leq n \leq 35$. The improved lower bounds come from two strategies. The first is a tabu search that operates at the level of bit swaps. The second is a novel greedy heuristic that repeatedly chooses the candidate codeword that maximizes a randomly-scored histogram of distances to previously-added codewords. These strategies were proposed by CPro1, an automated protocol that generates, implements, and tests diverse strategies for combinatorial constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00174 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automated Discovery of Improved Constant Weight Binary Codes Rosin, Christopher D. Information Theory Artificial Intelligence Discrete Mathematics Combinatorics A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code with parameters $n,d,w$. We establish improved lower bounds on $A(n,d,w)$ by constructing new larger codes, for 24 values of $(n,d,w)$ with $6 \leq d \leq 18$ and $18 \leq n \leq 35$. The improved lower bounds come from two strategies. The first is a tabu search that operates at the level of bit swaps. The second is a novel greedy heuristic that repeatedly chooses the candidate codeword that maximizes a randomly-scored histogram of distances to previously-added codewords. These strategies were proposed by CPro1, an automated protocol that generates, implements, and tests diverse strategies for combinatorial constructions. |
| title | Automated Discovery of Improved Constant Weight Binary Codes |
| topic | Information Theory Artificial Intelligence Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2603.00174 |