| 环F_l+vF_l上的二次剩余码 |
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| 引用本文： | 张涛,朱士信.环F_l+vF_l上的二次剩余码[J].中国科学技术大学学报,2012,42(3):207-213. |
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| 作者姓名： | 张涛 朱士信 |
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| 作者单位： | 1. 合肥工业大学数学学院,安徽合肥,230009
2. 合肥工业大学数学学院,安徽合肥230009;东南大学移动通信国家重点实验室,江苏南京210096 |
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| 基金项目： | 国家自然科学基金，教育部高校博士点基金 |
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| 摘 要： | 研究了环R=Fl+vFl(其中v2=v,且l是奇素数)上的二次剩余码.首先研究了环R上长为n的循环码,然后用生成幂等元的形式定义了环R上二次剩余码,并讨论了它们与其扩展码之间的关系和对偶等性质.进一步,定义并研究了环R上二次剩余码的极小Lee距离,结果表明环R上二次剩余码具有良好的参数.特别地,确定了F3+vF3上码长为11的二次剩余码的幂等生成元的具体形式和它们的极小Lee距离.
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| 关 键 词： | 循环码 二次剩余码 幂等生成元 对偶码 极小Lee距离 |
Quadratic residue code over Fl+vFl |
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| ZHANG Tao
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ZHU Shixin.Quadratic residue code over Fl+vFl[J].Journal of University of Science and Technology of China,2012,42(3):207-213. |
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| Authors: | ZHANG Tao ZHU Shixin |
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| Institution: | 1,2 (1.School of Mathematics,Hefei University of Technology,Hefei 230009,China; 2.National Mobile Communications Research Laboratory,Southeast University,Nanjing 210096,China) |
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| Abstract: | Quadratic residue codes over the ring R=Fl+vFl was investigated,where v2=v and l is an odd prime.Cyclic codes of length n over R was studied first.Then,quadratic residue codes over R was defined by their generating idempotents,and the relations between these codes and their extended codes were discussed.Their properties,including their duality were also studied.Further,their minimum Lee distance was defined and investigated,and good parameters were shown.In particular,the specific forms of generating idempotents of quadratic residue codes of length 11 over F3+vF3 were determined,and its minimum Lee distance was considered. |
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| Keywords: | cyclic codes quadratic residue codes generating idempotents dual codes minimum Lee distance |
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