Abstract
In this work we introduce a novel approach to find reversible codes over different alphabets, using so-called coterm polynomials and a module-construction. We obtain many optimal reversible codes with these constructions. In an attempt to apply the constructions to the DNA, we identify k-bases of DNA with elements in the ring R2k=F2[u]/(u2k−1), and by using a form of coterm polynomials, we are able to solve the reversibility and complement problems in DNA codes over this ring. With a freedom on the choice of k we are able to embed any DNA code in a suitable ring, giving an algebraic structure to the DNA codes. We are also able to find reversible and reversible-complement codes that are not necessarily linear cyclic codes.
Original language | English (US) |
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Pages (from-to) | 217-234 |
Number of pages | 18 |
Journal | Finite Fields and Their Applications |
Volume | 46 |
DOIs | |
State | Published - Jul 1 2017 |
Externally published | Yes |
Keywords
- Coterm polynomials
- DNA codes
- Reversible-complement codes
- Shift
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- General Engineering
- Applied Mathematics