We extend the Gau map andGau distance, defined in DKBG, over all the $16$ rings$\mathcal{R}__\theta . An isometry between the codes over the rings and the analogous DNA codes is established in general . We propose family of DNA codes that satisfies reverse and reverse-complement constraints using the Reed-Muller type codes . The technical contributions of this paper aretwofold. Considering the Generalized Gau distance, Sphere Packing-like bound,GV-like . bound, . Singleton like bound, Singleton . like bound and Plotkin .like bound are established overthe rings $mathcal {R]_\ theta . In addition to this, optimal class of codes areprovided with respect to .

Author(s) : Adel Alahmadi, Krishna Gopal Benerjee, Sourav Deb, Manish K Gupta

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Keywords : codes - bound - dna - rings - -

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