| 有限域上的重根自对偶负循环码 |
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| 引用本文： | 李秀丽. 有限域上的重根自对偶负循环码[J]. 数学研究及应用, 2016, 36(3): 275-284 |
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| 作者姓名： | 李秀丽 |
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| 作者单位： | 青岛科技大学数理学院, 山东 青岛 266000; 中国海洋大学信息科学与工程学院, 山东 青岛 266000 |
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| 基金项目： | 山东省中青年科学家奖励基金(Grant No.BS2011DX011),青岛市博士后基金(Grant No.861605040007). |
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| 摘 要： | Let F_q be a finite field with q = p~m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2~ap~r over F_q, a ≥ 1.The construction of self-dual negacyclic codes of length 2~abp~r over F_q is also provided, where gcd(2, b) = gcd(b, p) = 1 and a ≥ 1.
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| 关 键 词： | 常循环码 负循环码 自对偶码 生成多项式 |
| 收稿时间： | 2015-05-05 |
| 修稿时间： | 2016-01-13 |
Repeated-Root Self-Dual Negacyclic Codes over Finite Fields |
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| Xiuli LI. Repeated-Root Self-Dual Negacyclic Codes over Finite Fields[J]. Journal of Mathematical Research with Applications, 2016, 36(3): 275-284 |
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| Authors: | Xiuli LI |
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| Affiliation: | School of Mathematics and Physics, Qingdao University of Science and Technology, Shandong 266000, P. R. China; College of Information Science and Engineering, Ocean University of China, Shandong 266000, P. R. China |
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| Abstract: | Let $F_{q}$ be a finite field with $q=p^{m}$, where $p$ is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over $F_{q}$. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length $2^{a}p^{r}$ over $F_{q}$, $ageq1$. The construction of self-dual negacyclic codes of length $2^{a}bp^{r}$ over $F_{q}$ is also provided, where ${rm gcd}(2,b)={rm gcd}(b,p)=1$ and $ageq1$. |
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| Keywords: | constacyclic codes negacyclic codes self-dual codes generator polynomials |
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