Table of Contents
ISRN Biomathematics
Volume 2013, Article ID 538631, 8 pages
Research Article

Dinucleotide Circular Codes

1Equipe de Bioinformatique Théorique, BFO, LSIIT, UMR 7005, Université de Strasbourg, Pôle API, 300 Boulevard Sébastien Brant, 67400 Illkirch, France
2Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, Consiglio Nazionale delle Ricerche and Dipartimento di Matematica, “Ulisse Dini” Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
3Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France

Received 12 October 2012; Accepted 12 December 2012

Academic Editors: J. Chow, M. Jose, M. R. Roussel, and J. H. Wu

Copyright © 2013 Christian J. Michel and Giuseppe Pirillo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.