A necklace algorithm to determine the growth function of trinucleotide circular codes

Matthieu Luc Herrmann, Christian Michel, Benoît Sugmeyer

Research output: Contribution to journalArticleResearchpeer-review


Circular codes are mathematical objects studied in combinatorics - theoretical computer science, and theoretical biology. So far, there is no close formulas allowing to determine the growth function (number and list) of circular codes. This combinatorial problem can only be solved by an algorithmic approach. We propose a new algorithm based on a necklace proposition to determine the growth function of trinucleotide circular codes, a trinucleotide being a word of 3 letters on a 4-letter alphabet. This necklace algorithm, unique in its class, can be extended in future to the analysis of codes, e.g. circular codes, containing words greater than 3 letters and also over larger alphabets.
Original languageEnglish
Pages (from-to)1-40
JournalJournal of Applied Mathematics & Bioinformatics
Publication statusPublished - 2013
Externally publishedYes


  • Circular code
  • Genetic code
  • necklace algorithm
  • combinatorial algorithm

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