Mixed circular codes
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Updated: Jan 21, 2026

Identification of Coding and Non-coding RNA Classes Expressed in Swine Whole Blood
Published on: November 28, 2018
Elena Fimmel1, Christian J Michel2, François Pirot3
1Institute of Mathematical Biology, Faculty for Computer Sciences, Mannheim University of Applied Sciences, Mannheim 68163, Germany.
Abstract:
By an extensive statistical analysis in genes of bacteria, archaea, eukaryotes, plasmids and viruses, a maximal C3-self-complementary trinucleotide circular code has been found to have the highest average occurrence in the reading frame of the ribosome during translation. Circular codes may play an important role in maintaining the correct reading frame. On the other hand, as several evolutionary theories propose primeval codes based on dinucleotides, trinucleotides and tetranucleotides, mixed circular codes were investigated. By using a graph-theoretical approach of circular codes recently developed, we study mixed circular codes, which are the union of a dinucleotide circular code, a trinucleotide circular code and a tetranucleotide circular code. Maximal mixed circular codes of (di,tri)-nucleotides, (tri,tetra)-nucleotides and (di,tri,tetra)-nucleotides are constructed, respectively. In particular, we show that any maximal dinucleotide circular code of size 6 can be embedded into a maximal mixed (di,tri)-nucleotide circular code such that its trinucleotide component is a maximal C3-comma-free code. The growth function of self-complementary mixed circular codes of dinucleotides and trinucleotides is given. Self-complementary mixed circular codes could have been involved in primitive genetic processes.
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