Cyclic DNA codes over F2+uF2+vF2+uvF2

2015/08/28 by Shixin Zhu, Xiaojing Chen, Zhu, Shixin +1
Computer Science · Biochemistry, Genetics and Molecular Biology · #Coding theory and cryptography #DNA and Biological Computing #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.1508.07113

Abstract

In this work, we study the structure of cyclic DNA codes of arbitrary lengths over the ring R=F2+uF2+vF2+uvF2 and establish relations to codes over R1=F2+uF2 by defining a Gray map between R and R1² where R1 is the ring with 4 elements. Cyclic codes of arbitrary lengths over R satisfied the reverse constraint and the reverse-complement constraint are studied in this paper. The GC content constraint is considered in the last.

Related

• DNA Cyclic Codes Over The Ring \F₂[u,v]/⟨ u²-1,v³-v,uv-vu ⟩
• On cyclic DNA codes over \mathbbF₂+u\mathbbF₂+u²\mathbbF₂
• Construction of Cyclic Codes over mathbbF₂+u mathbbF₂ for DNA\n Computing
• Construction of cyclic DNA codes over the Ring \Z₄[u]/⟨ u²-1 ⟩ Based on the deletion distance
• On cyclic DNA codes over the Ring \Z₄ + u \Z₄