| 焦荣政,任文妮.代数函数域的一些Artin-Schreier型扩张相伴的Riemann-Roch空间[J].数学年刊A辑,2011,32(4):507~518 |
| 代数函数域的一些Artin-Schreier型扩张相伴的Riemann-Roch空间 |
| Riemann-Roch Spaces Attached to Artin-Schreier Extensions of Algebraic Function Fields |
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| DOI： |
| 中文关键词: 代数函数域 除子 Riemann-Roch空间 代数几何码 |
| 英文关键词:Algebraic function fields Divisor Riemann-Roch space AG code |
| 基金项目:国家留学基金委留学回国人员科研启动基金与扬州大学校基金的资助 |
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| 中文摘要: |
| 阐明给定代数函数域上一些除子的Riemann-Roch空间是代数几何码构造的基础. 给出代数函数域的一些Artin-Schreier型扩张的Riemann-Roch空间的一组基,并应用于编码理论,
得到$\mathbb{F}_{16}$上参数分别是[54,43,5], [54,41,7], [54,40,8]的代数几何码. |
| 英文摘要: |
| It is fundamental to get the Riemann-Roch spaces of certain kind of divisors before constructing AG codes.
Basis of Riemann-Roch spaces of kinds of divisors attached to Artin-Schreier extensions of algebraic function fields are explicitly computed in this paper. As an application, AG codes of [54,43,5], [54,41,7], [54,40,8] are constructed over $\mathbb{F}_{16}$. |
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