Cyclic DNA codes over $$\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2$$F2+uF2+vF2+uvF2 and their applications
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DOI: 10.1007/s12190-016-1046-3
Abstract: In this paper, we study the structure of cyclic DNA codes of arbitrary length over the ring $$R=\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2$$R=F2+uF2+vF2+uvF2, $$u^{2}=0, v^{2}=v, uv=vu$$u2=0,v2=v,uv=vu. By defining a Gray map, we establish a relation between… read more here.
Keywords: dna codes; mathbb uf2; mathbb mathbb; cyclic dna ... See more keywords
A BPSON Algorithm Applied to DNA Codes Design
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DOI: 10.1109/access.2019.2924708
Abstract: DNA computing proposed by Adelman is new biotechnology which provides a new way to solve NP-hard problem. It has a promising future and successful results of various applications. DNA codes design is a significant step… read more here.
Keywords: codes design; algorithm; dna codes; bpson ... See more keywords
New DNA Codes from Cyclic Codes over Mixed Alphabets
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DOI: 10.3390/math8111977
Abstract: Let R=F4+uF4,withu2=u and S=F4+uF4+vF4,withu2=u,v2=v,uv=vu=0. In this paper, we study F4RS-cyclic codes of block length (α,β,γ) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]⟨xα−1⟩×R[x]⟨xβ−1⟩×S[x]⟨xγ−1⟩. We discuss their generator… read more here.
Keywords: dna; dna codes; cyclic codes; cyclic dna ... See more keywords