| 一类Zp上的非线性码 |
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| 引用本文： | 董久祥,董学东,张妍.一类Zp上的非线性码[J].辽宁师范大学学报(自然科学版),2006,29(2):129-132. |
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| 作者姓名： | 董久祥 董学东 张妍 |
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| 作者单位： | 1. 东北大学,信息科学与工程学院,辽宁,沈阳,110004
2. 辽宁师范大学,数学学院,辽宁,大连,116029 |
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| 基金项目： | 国家自然科学基金资助项目（10171042） |
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| 摘 要： | Asch等人将Gray映射推广为Zp^2到Zp的等距映射并构造了两类Zp上的非线性码,其中p为奇素数,笔者进一步将Gray映射推广并将Zp^s（s≥2）上的一类线性码映射为Zp上的一类具有较大距离的非线性码,其中p为奇素效．
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| 关 键 词： | Gray映射 Galois环 非线性码 基本不可约多项式 |
| 文章编号： | 1000-1735(2006)02-0129-04 |
| 收稿时间： | 10 8 2005 12:00AM |
| 修稿时间： | 2005年10月8日 |
A Family of Nonlinear Codes over Zp |
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| DONG Jiu-xiang,DONG Xue-dong,ZHANG Yan.A Family of Nonlinear Codes over Zp[J].Journal of Liaoning Normal University(Natural Science Edition),2006,29(2):129-132. |
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| Authors: | DONG Jiu-xiang DONG Xue-dong ZHANG Yan |
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| Institution: | 1. School of Information Science and Engineering, Northeastern University, Shenyang 110004, China; 2. School of Mathematics, Liaoning Normal University, Dalian 116029, China |
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| Abstract: | A relation was established between linear codes over Z_4 and certain interesting non-linear binary codes of even length by means of the so called Gray map.Asch et al.generalized the Gray map to an isometry between Z_(p~2) and Z_p and constructed two "dual" families of nearly-linearly codes over Z_p,where p is an odd prime.We further generalize the Gray map and get a family of non-linear codes over Z_p,where p is an odd prime.These codes have large distances. |
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| Keywords: | Gray map Galois ring nonlinear codes basic irreducible polynomial |
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