A classification of 20-trinucleotide circular codes

Authors:
Christian J. Michel;Giuseppe Pirillo;Mario A. Pirillo
Affiliations:
Equipe de Bioinformatique Théorique, BFO, LSIIT (UMR 7005), Université de Strasbourg, Pôle API, Boulevard Sébastien Brant, 67400 Illkirch, France;CNR, IASI, Unití di Firenze, Dipartimento di Matematica "U. Dini", viale Morgagni 67/A, 50134 Firenze, Italy and Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Marne-la ...;Istituto Statale SS. Annunziata, Piazzale del Poggio Imperiale, 50134 Firenze, Italy
Venue:
Information and Computation
Year:
2012

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Abstract

Trinucleotide comma-free codes and trinucleotide circular codes are two important classes of codes in code theory and theoretical biology. A trinucleotide circular code containing exactly 20 elements is called here a 20-trinucleotide circular code. In this paper, solving a combinatorial problem of hard computational complexity, we extend and improve our results of C.J. Michel, G. Pirillo, and M.A. Pirillo (2008) [14] concerning the small class of 528 self-complementary 20-trinucleotide circular codes, to the complete class of the 20-trinucleotide circular codes which contains 12,964,440 elements. A surprising relation with the symmetric group @S"4 appears but it remains unexplained so far.