| 有限主理想环上的MDR码 |
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| 引用本文： | 唐刚,张晓燕.有限主理想环上的MDR码[J].山西大学学报(自然科学版),2012,35(1):21-23. |
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| 作者姓名： | 唐刚 张晓燕 |
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| 作者单位： | 黄石理工学院数理学院,湖北黄石,435003 |
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| 基金项目： | 湖北省教育厅自然科学基金(B20114410) |
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| 摘 要： | 设R是具有最大理想〈γ〉的有限链环,C为R上的线性码.定义S(C)={u∈C│γu=0｝.本文证明了R上码C为MDR码当且仅当S(C)为剩余类域F=R/〈γ〉上的MDS码.进一步地,若S(C1),…,S(Ct)分别为有限链环R1,…,Rt的剩余类城F1,…,Ft的MDS码,则C=CRT(C1,…,Ct)为主理想环R=CRT(R1,…,Rt)上的MDR码.
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| 关 键 词： | 有限链环 有限主理想环 MDR码 |
MDR Codes Over Finite Principal Ideal Rings |
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| TANG Gang
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ZHANG Xiao-yan.MDR Codes Over Finite Principal Ideal Rings[J].Journal of Shanxi University (Natural Science Edition),2012,35(1):21-23. |
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| Authors: | TANG Gang ZHANG Xiao-yan |
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| Institution: | ( School of Mathematics and Physics,Huangshi Institute of Technology,Huangshi 435003,China) |
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| Abstract: | Let R be a finte chain ring with maximal ideal 〈γ〉,and let C be a linear code over R.We define S(C)={u∈C|γu=0}.We prove that the code C over R is MDR if and only if S(C) is MDS over residue field F=R/〈γ〉 of R.Moreover,if S(Cj) is MDS over residue field Fj of finite chain ring Rj,for j=1,…,t,then C=CRT(C1,…,Ct) is MDR over the finite principal ideal ring R=CRT(R1,…,Rt). |
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| Keywords: | finite chain rings finite principal ideal rings MDRcodes |
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