A Free Group Approach to Error Correction

In this brief exploratory paper, we present a novel free group based method for error correction, making use of the universal property of free groups (UPFG). Through example, we show that, in certain scenarios, our method of error correction is more efficient and more deterministic than minimum distance error correction. We argue that our method works well under specific conditions that have been shown to have been met by certain neural systems. We hope that this might interest others in the role free groups may play in understanding how error correction of neural codes works.