Cyclic and Quasi-Cyclic DNA Codes

10/19/2021

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by   Adel Alahmadi, et al.

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In this paper, we discuss DNA codes that are cyclic or quasi-cyclic over _4+ω_4, where ω^2=2+2ω along with methods to construct these with combinatorial constraints. We also generalize results obtained for the ring _4+ω_4, where ω^2=2+2ω, and some other rings to the sixteen rings R_θ=_4+ω_4, where ω^2=θ∈_4+ω_4, using the generalized Gau map and Gau distance in <cit.>. We determine a relationship between the Gau distance and Hamming distance for linear codes over the sixteen rings R_θ which enables us to attain an upper boundary for the Gau distance of free codes that are self-dual over the rings R_θ.