Abstract: To reduce the total amount of linear sequence (DNA, RNA or other medium) required to encode a set of genetic elements, the present disclosure describes a computational method for compressing genetic information by finding one or more sequences that each mutually encode multiple genetic elements in the same stretch of sequence (a “co-encoding”). The computational method encodes each of the genetic elements in respective directed acyclic graphs (DAGs) or finite automatons (FAs), then encodes overlapping sequences between the DAGs or FAs in a second DAG or FA. Additional DAGs or FAs may be encoded for overlapping sequences that result from shifting the reading frame of the genetic elements relative to one another and switching the orientation of the elements.