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Trinucleotide k-circular codes I: Theory.

Christian J Michel1, Baptiste Mouillon1, Jean-Sébastien Sereni1

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Summary
This summary is machine-generated.

This study introduces algorithms to analyze k-circular codes, specifically trinucleotide codes. Researchers determined growth functions for these codes, crucial for understanding their combinatorial properties and applications.

Keywords:
AlgorithmCircular codeCodeGraphGrowth functionk-circular code

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Area of Science:

  • Coding Theory
  • Combinatorics
  • Bioinformatics

Background:

  • Understanding the structure of codes is essential in various fields, including data compression and bioinformatics.
  • Circular codes possess unique properties related to reading frame retrieval, particularly in biological sequences like trinucleotides.

Purpose of the Study:

  • To develop and apply novel algorithms for analyzing k-circular codes, with a focus on trinucleotide codes.
  • To determine the growth functions of trinucleotide k-circular codes for k values from 0 to 4.
  • To investigate these properties in general and specific cases, including minimum, maximal, and self-complementary codes.

Main Methods:

  • Development of three distinct algorithmic approaches: directed graph cycle analysis (directed girth), eigenvalue computation of matrices, and incremental file-based result saving.
  • Application of these algorithms to verify computational results and analyze the combinatorics of trinucleotide k-circular codes.

Main Results:

  • The study successfully determined the growth functions for trinucleotide k-circular codes for k = 0, 1, 2, 3, and 4.
  • The developed algorithms provide a robust method for verifying computational results in this complex area.
  • Insights into the growth functions of various specific types of k-circular codes were obtained.

Conclusions:

  • The research provides a comprehensive analysis of trinucleotide k-circular codes and their growth functions.
  • The developed algorithmic frameworks offer efficient tools for studying complex coding structures.
  • This work contributes to a deeper understanding of the combinatorial properties of circular codes with potential applications in sequence analysis.