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

摘要

Circularcodes are mathematical objects studied in combinatorics - theoretical computerscience, and theoretical biology. So far, there is no close formulas allowingto determine the growth function (number and list) of circular codes. Thiscombinatorial problem can only be solved by an algorithmic approach. We proposea new algorithm based on a necklace proposition to determine the growthfunction of trinucleotide circular codes, a trinucleotide being a word of 3letters 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.