Linear constructions for DNA codes
Theoretical Computer Science
Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom---Tsfasman Metric
Designs, Codes and Cryptography
Cyclic Codes over the Integers Modulopm
Finite Fields and Their Applications
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The structure of DNA is used as a model for constructing good error correcting codes and conversely error correcting codes that enjoy similar properties with DNA structure are also used to understand DNA itself. Recently, naturally four element sets are used to model DNA by some families of error correcting codes. Hence the structure of such codes has been studied. In this paper, the authors first relate DNA pairs with a special 16 element ring. Then, the so-called cyclic DNA codes of odd length that enjoy some of the properties of DNA are studied. Their algebraic structure is determined. Further, by introducing a map, a family of cyclic codes over this ring is mapped to DNA codes. Hamming minimum distances are also studied. The paper concludes with some DNA examples obtained via this family of cyclic codes.