Geometric Orthogonal Codes of Size Larger Than Optical Orthogonal Codes

The class of geometric orthogonal codes (GOCs) was introduced by Doty and Winslow (2016) for more robust macrobonding in DNA origami. They observed that GOCs are closely related to optical orthogonal codes (OOCs). It is possible for GOCs to have size greater than OOCs of corresponding parameters due to slightly more relaxed constraints on correlations. However, the existence of GOCs exceeding the size of optimal OOCs of corresponding parameters has never been demonstrated. This paper gives the first infinite family of GOCs of size greater than optimal OOCs.