# Automated Discovery of Improved Constant Weight Binary Codes

arXiv: https://arxiv.org/abs/2603.00174 · HTML: https://mlsanity.com/paper/2603.00174/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 4 of 4)

- [Using Code Generation to Solve Open Instances of Combinatorial Design Problems](https://mlsanity.com/paper/2501.17725/) (2025)
- [LLM-Guided Search for Deletion-Correcting Codes](https://mlsanity.com/paper/2504.00613/) (2025)
- [Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems](https://mlsanity.com/paper/2505.23881/) (2025)
- [Improved Upper Bounds for Slicing the Hypercube](https://mlsanity.com/paper/2602.16807/) (2026)

## Abstract (arXiv)

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 ≤ d ≤ 18 and 18 ≤ n ≤ 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.