Construction of Cyclic Codes over $${\mathbb {Z}}_{20}$$ for Identifying Proteins

For biology, engineering and biotechnology, among others sciences related with the subject, it is essential to understand the role of proteins in the genetic information transmission process in order to conclude about evolution, changes, and connection between species. In recent work, protein synthesis process has been compared with a digital transmission system and, thus, algorithms which allow identifying biological sequences as code-words of BCH codes were developed to verify the validity of this model. Algorithms in literature are limited in respect to the length of the biological sequence, which creates restrictions when establishing taxonomic and phylogenetic inferences of living beings. In this work, we extend the number of sequences that can be analyzed by designing an algorithm that identifies, using cycling codes, biological sequences with odd length and, thus, it makes possible to find a relation between mathematical properties of cycling codes with biological properties (taxonomy and phylogeny).