环F_4[v]/(v~2+v)上DNA码
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摘要
文章研究了环R=F_4[v]/(v~2+v)上的DNA码.基于环R上长度为n的线性码的代数结构,给出了环R上长度为n的线性码是可逆的DNA码的一个充要条件.同时,给出了环R上长度为n的线性码是可逆补DNA码的一个充要条件.
DNA codes over the ring R=F_4[v]/(v~2+v) are studied. Based on the algebraic structure of the linear codes of length n over the ring R, we give a necessary and sufficient condition for the linear codes of length n over the ring R to be reversible DNA codes. And we give a necessary and sufficient condition for the linear codes of length n over the ring R to be reversible-complement DNA codes.
DNA codes over the ring R=F_4[v]/(v~2+v) are studied. Based on the algebraic structure of the linear codes of length n over the ring R, we give a necessary and sufficient condition for the linear codes of length n over the ring R to be reversible DNA codes. And we give a necessary and sufficient condition for the linear codes of length n over the ring R to be reversible-complement DNA codes.
引文
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[4] Abualrub T,Ghrayeb A,Zeng X.Construction of cyclic codes over GF(4) for DNA computing[J].J Franklin Inst.,2006,343(4-5):448-457.
[5] Siap I,Abualrub T,Ghrayeb A.Cyclic DNA codes over the ring F2[u]/(u2-1) based on the deletion distance [J].J Franklin Inst.,2009,346(8):731-740.
[6] Guenda K,Gulliver T A.Construction of cyclic codes over F2+uF2for DNA computing [J].Appl Algebr Eng Comm Comput,2013,24(6):445-459.
[7] Liang J,Wang L.On cyclic DNA codes over F2+uF2[J].J Appl Math Comput,2016,51(1-2):81-91.
[8] 陆坤凤,李富林.环F2+uF2上长度为2e的循环码的符号对距离[J].大学数学,2017,33(6):1-6.
[9] 开晓山,朱士信.有限交换环上常循环码研究[J].大学数学,2016,32(2):1-7.
[10] Yildiz B,Siap I.Cyclic codes over F2[u]/(u4-1)and applications to DNA codes [J].Comput Math Appl,2012,63(7):1169-1176.
[11] Oztas E S,Siap I.Lifted polynomials over F16 and their applications to DNA codes [J].Filomat,2013,27(3):459-466.
[12] Bayram A,Oztas E S,Siap I.Codes over F4+vF4 and some DNA applications [J].Des Codes Cryptogr,2016,80(2):379-393.
[13] Zhu S,Wang L.A class of constacyclic codes over Fp+vFp and its Gray image [J].Discrete Mathematics,2011,311:2677-2682.
[2] Rykovv V V,Macula A J,Tomey D C,etal.DNA sequences and quaternary cyclic codes [C]//IEEE International Symposium on Information Theory.Washington DC:2001:248.
[3] Gaborit P,King O D.Linear construction for DNA codes [J].Theoretical Computer Science,2005,334:99-113.
[4] Abualrub T,Ghrayeb A,Zeng X.Construction of cyclic codes over GF(4) for DNA computing[J].J Franklin Inst.,2006,343(4-5):448-457.
[5] Siap I,Abualrub T,Ghrayeb A.Cyclic DNA codes over the ring F2[u]/(u2-1) based on the deletion distance [J].J Franklin Inst.,2009,346(8):731-740.
[6] Guenda K,Gulliver T A.Construction of cyclic codes over F2+uF2for DNA computing [J].Appl Algebr Eng Comm Comput,2013,24(6):445-459.
[7] Liang J,Wang L.On cyclic DNA codes over F2+uF2[J].J Appl Math Comput,2016,51(1-2):81-91.
[8] 陆坤凤,李富林.环F2+uF2上长度为2e的循环码的符号对距离[J].大学数学,2017,33(6):1-6.
[9] 开晓山,朱士信.有限交换环上常循环码研究[J].大学数学,2016,32(2):1-7.
[10] Yildiz B,Siap I.Cyclic codes over F2[u]/(u4-1)and applications to DNA codes [J].Comput Math Appl,2012,63(7):1169-1176.
[11] Oztas E S,Siap I.Lifted polynomials over F16 and their applications to DNA codes [J].Filomat,2013,27(3):459-466.
[12] Bayram A,Oztas E S,Siap I.Codes over F4+vF4 and some DNA applications [J].Des Codes Cryptogr,2016,80(2):379-393.
[13] Zhu S,Wang L.A class of constacyclic codes over Fp+vFp and its Gray image [J].Discrete Mathematics,2011,311:2677-2682.