Constructing Double Cyclic Codes over for DNA Codes

Area of Science:

• Algebraic coding theory
• Bioinformatics
• Computational biology

Background:

• Double cyclic codes are a class of codes with applications in data storage and communication.
• DNA computing and DNA data storage leverage the unique properties of DNA molecules for information processing and storage.
• Existing coding techniques may not fully meet the specific requirements for reliable DNA data storage.

Purpose of the Study:

• To investigate the algebraic structure of double cyclic codes over finite fields.
• To develop a framework for constructing DNA codes from double cyclic codes.
• To determine the conditions under which these DNA codes exhibit desired properties like reversibility.

Main Methods:

• Analysis of the algebraic properties of double cyclic codes.
• Development of a construction methodology for DNA codes based on double cyclic codes.
• Derivation of necessary and sufficient conditions for reversibility and reversible-complement properties.

Main Results:

• Characterization of the algebraic structure of double cyclic codes.
• A systematic method for generating DNA codes from these codes.
• Identification of specific conditions ensuring reversibility and reversible-complement properties in the constructed DNA codes.

Conclusions:

• Double cyclic codes provide a viable algebraic foundation for constructing DNA codes.
• The established conditions facilitate the design of robust and error-resilient DNA data storage systems.
• The presented DNA code examples demonstrate the practical applicability of the theoretical findings.