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Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
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DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/〈v3〉.

Om Prakash1, Ashutosh Singh1, Ram Krishna Verma2

  • 1Department of Mathematics, Indian Institute of Technology Patna, Bihar 801106, India.

Entropy (Basel, Switzerland)
|February 25, 2023
PubMed
Summary
This summary is machine-generated.

This study explores reversible and DNA codes, developing new codes with improved parameters using algebraic structures and Gray maps. The research enhances coding theory with better DNA code performance and distance metrics.

Keywords:
DNA codesgray mapreversible code

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Area of Science:

  • Coding Theory
  • Algebraic Geometry
  • Bioinformatics

Background:

  • Cyclic and skew cyclic codes are fundamental in coding theory.
  • Chain rings provide a structure for constructing codes with specific properties.
  • DNA codes are essential for biological applications and data storage.

Purpose of the Study:

  • To investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]/⟨v3⟩.
  • To associate codons with elements of R using a Gray map.
  • To obtain new reversible and DNA codes with improved parameters.

Main Methods:

  • Utilizing a Gray map to link codons with elements of the ring R.
  • Analyzing the structure of cyclic and skew cyclic codes over the specified chain ring.
  • Determining the Hamming and Edit distances of the newly derived codes.

Main Results:

  • Established an association between codons and elements of R via a Gray map.
  • Developed several new DNA codes with superior parameters compared to existing codes.
  • Successfully determined the Hamming and Edit distances for these novel codes.

Conclusions:

  • The study successfully generated new reversible and DNA codes with enhanced parameters.
  • The use of algebraic structures and Gray maps proved effective for code construction.
  • The obtained codes offer improved performance for applications in bioinformatics and data storage.