Coding Agents for Coding Theory

We spent five weeks using an LLM coding agent on open problems in coding theory: finding large sets of four-letter words, such as DNA barcodes, that stay far apart in edit distance. The agent wrote the verifiers and search code; a human chose the problem and set the verification protocol. Restricting the search to codes with a prescribed symmetry, a classical technique, shrank the problem about fourfold and raised the best known code of length $6$ and minimum edit distance $3$ from $114$ to $120$ words ($E_4(6,3) \ge 120$). The same pipeline improved twelve further lower bounds at lengths $6$ to $9$ and distances $3$ to $6$. We give the failures equal space. Our own search stopped at $116$ and recorded the last symmetry class as topping out at $112$; a second agent session, running the same search with a better operator, found the $120$. A later verdict that the method did not carry over to length $7$ was wrong for the same reason, and an earlier instance cost three weeks. Each time, an intermediate result was written down, never rechecked, and treated as a fact that ruled out further search. Checking final outputs, as our protocol required, does not catch such errors.