Dinucleotide Circular Codes

Abstract

We begin here a combinatorial study of dinucleotide circular codes. A word written on a circle is called circular. A set of dinucleotides is a circular code if all circular words constructed with this set have a unique decomposition. Propositions based on a letter necklace allow to determine the 24 maximum dinucleotide circular codes (of 6 elements). A partition property is also identified with eight self-complementary maximum dinucleotide circular codes and two classes of eight maximum dinucleotide circular codes in bijective correspondence by the complementarity map.