一種構造GC常重量DNA碼的方法
doi: 10.11999/JEIT190070
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1.
安徽新華學院通識教育部 合肥 230088
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2.
福建師范大學數(shù)學與信息學院 福州 350117
基金項目: 安徽省高校自然科學研究項目(KJ2017A623，KJ2018A0584)，安徽新華學院自然科學重點項目(2018zr001)
A Method for Constructing GC Constant Weight DNA Codes
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Ministry of General Education, Anhui Xinhua University, Hefei 230088, China
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College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China
Funds: Anhui University Natural Science Research Project (KJ2017A623, KJ2018A0584), Anhui Xinhua University Natural Science Key Project (2018zr001)
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摘要: GC重量是DNA碼的一個重要參數(shù)，如何構造滿足GC常重量約束的DNA碼是一個有趣的問題。該文通過在DNA碼與四元碼之間建立一個雙射，將構造滿足GC常重量約束的DNA碼轉化為構造GC常重量四元碼。通過代數(shù)的方法，構造了3類滿足GC常重量約束的DNA碼。Abstract: GC weight is an important parameter of DNA code, and how to meet GC constant weight constraint DNA code is an interesting problem. In this paper, by establishing a bijection between DNA code and quaternion code, the DNA code that satisfies the GC constant weight constraint is converted into a GC constant weight quaternary code. Through the algebraic method, three types of DNA codes that meet the constant weight constraints of GC are constructed.
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Key words:
- Quaternary code /
- DNA code /
- GC weight
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ADLEMAN L M. Molecular computation of solutions to combinatorial problems[J]. Science, 1994, 266(5187): 1021–1024. doi: 10.1126/science.7973651 FRUTOS A G, LIU Qinghua, THIEL A J, et al. Demonstration of a word design strategy for DNA computing on surfaces[J]. Nucleic Acids Research, 1997, 25(23): 4748–4757. doi: 10.1093/nar/25.23.4748 MARATHE A, CONDON A E, and CORN R M. On combinatorial DNA word design[J]. Journal of Computational Biology, 2001, 8(3): 201–220. doi: 10.1089/10665270152530818 RYKO V V, MACULA A J, TORNEY D C, et al. DNA sequences and quaternary cyclic codes[C]. 2001 IEEE International Symposium on Information. Washington, USA, 2001: 248–248. GABORIT P and KING O D. Linear constructions for DNA codes[J]. Theoretical Computer Science, 2005, 334(1/3): 99–113. doi: 10.1016/j.tcs.2004.11.004 ABUALRUB T, GHRAYEB A, and ZENG Xiangnian. Construction of cyclic codes over GF(4) for DNA computing[J]. Journal of the Franklin Institute, 2006, 343(4/5): 448–457. doi: 10.1016/j.jfranklin.2006.02.009 SIAP I, ABUALRUB T, and GHRAYEB A. Cyclic DNA codes over the ring ${F_2}\left[ u \right]/\left( {{u^2} - 1} \right)$ based on the deletion distance[J]. Journal of the Franklin Institute, 2009, 346(8): 731–740. doi: 10.1016/j.jfranklin.2009.07.002GUENDA K and GULLIVER T A. Construction of cyclic codes over ${{\mathbb{F}}_{2}}+u{{\mathbb{F}}_{2}}$ for DNA computing[J]. Applicable Algebra in Engineering, Communication and Computing, 2013, 24(6): 445–459. doi: 10.1007/s00200-013-0188-xLIANG Jing and WANG Liqi. On cyclic DNA codes over ${{\mathbb{F}}_{2}}+u{{\mathbb{F}}_{2}}$ [J]. Journal of Applied Mathematics and Computing, 2016, 51(1/2): 81–91. doi: 10.1007/s12190-015-0892-8ZHU Shixin and CHEN Xiaojing. Cyclic DNA codes over ${{\mathbb{F}}_{2}}+u{{\mathbb{F}}_{2}}+v{{\mathbb{F}}_{2}}+uv{{\mathbb{F}}_{2}}$ and their applications[J]. Journal of Applied Mathematics and Computing, 2017, 55(1/2): 479–493. doi: 10.1007/s12190-016-1046-3DINH H Q, SINGH A K, PATTANAYAK S, et al. Cyclic DNA codes over the ring ${{\mathbb{F}}_{2}}+u{{\mathbb{F}}_{2}}+v{{\mathbb{F}}_{2}}+ uv{{\mathbb{F}}_{2}}+$ ${{\rm{v}}^{\rm{2}}}{{\mathbb{F}}_{2}}+u{{v}^{2}}{{\mathbb{F}}_{2}}$ [J]. Designs, Codes and Cryptography, 2018, 86(7): 1451–1467. doi: 10.1007/s10623-017-0405-xSHI Minjia and LU Yaqi. Cyclic DNA codes over ${{\mathbb{F}}_{2}}[u,v]/<{{u}^{3}},{{v}^{2}}-v,vu-uv>$ [J]. Advances in Mathematics of Communications, 2019, 13(1): 157–164. doi: 10.3934/amc.2019009SINGH A K, KUMAR N, MISHRA P, et al. Construction of dual cyclic codes over ${{\mathbb{F}}_{2}}[u,v]/\left\langle {{u}^{2}},{{v}^{2}}-v,uv-vu \right\rangle $ for DNA Computation[J]. Defence Science Journal, 2018, 68(5): 467–472. doi: 10.14429/dsj.68.12344OZTAS E S, YILDIZ B, and SIAP I. A novel approach for constructing reversible codes and applications to DNA codes over the ring ${{{\mathbb{F}}_{2}}[u]}/{<{{u}^{2k}}-1>}\;$ [J]. Finite Fields and Their Applications, 2017, 46: 217–234. doi: 10.1016/j.ffa.2017.04.001LIDL R and NIEDERREITE H. Finite Fields[M]. New York: Addison-Wesley Publishing Company, 1983. -
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