International Journal of Combinatorics
Volume 2011 (2011), Article ID 659567, 14 pages
http://dx.doi.org/10.1155/2011/659567
Research Article

Strong Trinucleotide Circular Codes

Christian J. Michel1 and Giuseppe Pirillo2,3

1Equipe de Bioinformatique Théorique, FDBT, LSIIT (UMR UdS-CNRS 7005), Université de Strasbourg, Pôle API, boulevard Sébastien Brant, 67400 Illkirch, France
2Consiglio Nazionale delle Ricerche, Unità di Firenze, Dipartimento di Matematica “U.Dini”, Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, viale Morgagni 67/A, 50134 Firenze, Italy
3Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France

Received 5 February 2011; Accepted 25 April 2011

Academic Editor: Toufik Mansour

Copyright © 2011 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.

Abstract

Recently, we identified a hierarchy relation between trinucleotide comma-free codes and trinucleotide circular codes (see our previous works). Here, we extend our hierarchy with two new classes of codes, called 𝐷 𝐿 𝐷 and 𝐿 𝐷 𝐿 codes, which are stronger than the comma-free codes. We also prove that no circular code with 20 trinucleotides is a 𝐷 𝐿 𝐷 code and that a circular code with 20 trinucleotides is comma-free if and only if it is a 𝐿 𝐷 𝐿 code. Finally, we point out the possible role of the symmetric group ∑ 4 in the mathematical study of trinucleotide circular codes.