bansari rao

The idea of computing with DNA was given by Tom Head in 1987, however in 1994 in a seminal paper, the actual successful experiment for DNA computing was performed by Adleman. The heart of the DNA computing is the DNA hybridization, however, it is also the source of errors. Thus the success of the DNA computing depends on the error control techniques. The classical coding theory techniques have provided foundation for the current information and communication technology (ICT). Thus it is natural to expect that coding theory will be the foundational subject for the DNA computing paradigm. For the successful experiments with DNA computing usually we design DNA strings which are sufficiently dissimilar. This leads to the construction of a large set of DNA strings which satisfy certain combinatorial and thermodynamic constraints. Over the last 16 years, many approaches such as combinatorial, algebraic, computational have been used to construct such DNA strings. In this work, we survey th...

In this work, we study the DNA codes arising from the ring $R=c{Z}_{4}+w\mathbf{Z}_{4}$, where $w^{2}=2+2w$ with 16 elements. We establish a one to one correspondence, between the elements of the ring $R$ and all the DNA words of length 2, by defining a distance preserving Gau map $\phi$. Using this map, we give several new classes of DNA codes which are reversible and reversible-complement. We also give general conditions on the generator matrix of a code over $R$ which produces DNA codes with the required properties using the Gau map. Some of the constructed DNA codes are optimal.

In this work, we study the DNA codes from the ring R = Z4 + wZ4, where w 2 = 2 + 2w with 16 elements. We establish a one to one correspondence between the elements of the ring R and all the DNA codewords of length 2 by defining a distance preserving Gau map φ. Using this map, we give several new classes of the DNA codes which satisfies reverse and reverse complement constraints. Some of the constructed DNA codes are optimal.