A relation between trinucleotide comma-free codes and trinucleotide circular codes

The comma-free codes and circular codes are two important classes of codes in code theory and in genetics. Fifty years ago before the discovery of the genetic code, a trinucleotide (triletter) comma-free code was proposed for associating the codons of genes with the amino acids of proteins. More recently, in the last ten years, trinucleotide circular codes have been identified statistically in different genomes. Here, we identify a relation between these two classes of trinucleotide codes by constructing a hierarchy of comma-free and circular codes.