Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: DNA Codes over the Ring $\mathbb{Z}_4 + w\mathbb{Z}_4$   In this present work, we generalize the study of construction of DNA codes
over the rings $\mathcal{R}_\theta=\mathbb{Z}_4+w\mathbb{Z}_4$, $w^2 = \theta $
for $\theta \in \mathbb{Z}_4+w\mathbb{Z}_4$. Rigorous study along with
characterization of the ring structures is presented. We extend the Gau map and
Gau distance, defined in \cite{DKBG}, over all the $16$ rings
$\mathcal{R}_\theta$. Furthermore, an isometry between the codes over the rings
$\mathcal{R}_\theta$ and the analogous DNA codes is established in general.
Brief study of dual and self dual codes over the rings is given including the
construction of special class of self dual codes that satisfy reverse and
reverse-complement constraints. The technical contributions of this paper are
twofold. Considering the Generalized Gau distance, Sphere Packing-like bound,
GV-like bound, Singleton like bound and Plotkin-like bound are established over
the rings $\mathcal{R}_\theta$. In addition to this, optimal class of codes are
provided with respect to Singleton-like bound and Plotkin-like bound. Moreover,
the construction of family of DNA codes is proposed that satisfies reverse and
reverse-complement constraints using the Reed-Muller type codes over the rings
$\mathcal{R}_\theta$.

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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th