2 research outputs found

    On DNA Codes Over the Non-Chain Ring Z4+uZ4+u2Z4\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4 with u3=1u^3=1

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    In this paper, we present a novel design strategy of DNA codes with length 3n3n over the non-chain ring R=Z4+uZ4+u2Z4R=\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4 with 6464 elements and u3=1u^3=1, where nn denotes the length of a code over RR. We first study and analyze a distance conserving map defined over the ring RR into the length-33 DNA sequences. Then, we derive some conditions on the generator matrix of a linear code over RR, which leads to a DNA code with reversible, reversible-complement, homopolymer 22-run-length, and w3n\frac{w}{3n}-GC-content constraints for integer ww (0≤w≤3n0\leq w\leq 3n). Finally, we propose a new construction of DNA codes using Reed-Muller type generator matrices. This allows us to obtain DNA codes with reversible, reversible-complement, homopolymer 22-run-length, and 23\frac{2}{3}-GC-content constraints.Comment: This paper has been presented in IEEE Information Theory Workshop (ITW) 2022, Mumbai, INDI

    Skew cyclic codes over Z4+vZ4\mathbb{Z}_4+v\mathbb{Z}_4 with derivation: structural properties and computational results

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    In this work, we study a class of skew cyclic codes over the ring R:=Z4+vZ4,R:=\mathbb{Z}_4+v\mathbb{Z}_4, where v2=v,v^2=v, with an automorphism θ\theta and a derivation Δθ,\Delta_\theta, namely codes as modules over a skew polynomial ring R[x;θ,Δθ],R[x;\theta,\Delta_{\theta}], whose multiplication is defined using an automorphism θ\theta and a derivation Δθ.\Delta_{\theta}. We investigate the structures of a skew polynomial ring R[x;θ,Δθ].R[x;\theta,\Delta_{\theta}]. We define Δθ\Delta_{\theta}-cyclic codes as a generalization of the notion of cyclic codes. The properties of Δθ\Delta_{\theta}-cyclic codes as well as dual Δθ\Delta_{\theta}-cyclic codes are derived. As an application, some new linear codes over Z4\mathbb{Z}_4 with good parameters are obtained by Plotkin sum construction, also via a Gray map as well as residue and torsion codes of these codes.Comment: 25 page
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