Riemann-Roch空间与线性网络码
Riemann-Roch Spaces and Linear Network Codes
摘要：
我们利用有限域上的代数曲线和某些相关的Riemann-Roch空间构造线性网络码，并给出了获得其参数的方法。特别是，我们对待埃尔米特曲线和曲线与铃木和Ree组都具有最大数量的点的曲线，其各自的属。线性网络编码根据向量空间的基础来发送信息，并且该信息被接收为可能改变的向量空间的基础。作者声明：Frank R. Kschischang % \cite{DBLP:journals/tit/KoetterK08}介绍了一个度量的向量空间的集合，并表明，一个最小距离解码器，这个度量实现正确的解码，如果发送和接收的向量空间的交集的尺寸是足够大的。我们构造的向量空间在上述度量中具有从下到上的最小距离，这使得它们适合于线性网络编码。
英文摘要：
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated with the Suzuki and Ree groups all having the maximal number of points for curves of their respective genera. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang %\cite{DBLP:journals/tit/KoetterK08} introduced a metric on the set of vector spaces and showed that a minimal distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The vector spaces in our construction have minimal distance bounded from below in the above metric making them suitable for linear network coding.
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