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On Optimal and Quantum Code Construction from Cyclic Codes over F<sub>q</sub><i>PQ</i> with Applications.

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On Double Cyclic Codes over Finite Chain Rings for DNA Computing.

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This study explores double cyclic codes over a finite chain ring, constructing DNA codes with reversibility and reverse-complement properties using a generalized Gray map.

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DNA codechain ringdouble cyclic codereversible codereversible-complement code

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Area of Science:

  • Algebraic coding theory
  • Computational biology
  • Finite fields and rings

Background:

  • Double cyclic codes are essential in coding theory.
  • Finite chain rings offer unique algebraic structures.
  • DNA codes require specific properties like reversibility.

Purpose of the Study:

  • Investigate the algebraic structure of double cyclic codes over the finite chain ring Re.
  • Construct DNA codes from these double cyclic codes.
  • Establish criteria for reversibility and reverse-complement properties.

Main Methods:

  • Utilized the finite chain ring Re = F4e+vF4e (v2=0).
  • Developed a generalized Gray map from F2+vF2 to Re.
  • Applied algebraic structures to derive DNA code properties.

Main Results:

  • Characterized the algebraic structure of double cyclic codes over Re.
  • Successfully constructed DNA codes with desired properties.
  • Provided criteria for reversibility and reverse-complement properties.

Conclusions:

  • The study successfully links algebraic structures of double cyclic codes to DNA code properties.
  • The generalized Gray map provides an effective tool for DNA code construction.
  • Demonstrated the generation of reversible and reverse-complement DNA codes over Re.