Riemann-Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences
Riemann-Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences
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DOI：
10.1016/j.jpaa.2004.06.010
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发表时间：
2005-02
影响因子：
0.8
通讯作者：
Hiren Maharaj;Gretchen L. Matthews;G. Pirsic
中科院分区：
文献类型：
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作者：
Hiren Maharaj;Gretchen L. Matthews;G. Pirsic
本文讨论了Riemann-Roch空间基的两个应用。在第一个应用中，我们定义了一个因子的地板，并获得了改进的代数几何码的参数上界。这些界限适用于比Homma和Kim（J.Pure Appl.Algebra 162（2001）273）更大的一类代码。然后我们确定埃尔米特函数场的大类Riemann-Roch空间的显式基。这些基地给出了更好的估计的一大类m-点埃尔米特码的参数。在第二个应用程序中，这些基地用于快速实现Xing和Niederreiter的方法（Acta.阿里斯72（1995）281）用于构建低差异序列。
This paper is concerned with two applications of bases of Riemann–Roch spaces. In the first application, we define the floor of a divisor and obtain improved bounds on the parameters of algebraic geometry codes. These bounds apply to a larger class of codes than that of Homma and Kim (J. Pure Appl. Algebra 162 (2001) 273). Then we determine explicit bases for large classes of Riemann–Roch spaces of the Hermitian function field. These bases give better estimates on the parameters of a large class of m-point Hermitian codes. In the second application, these bases are used for fast implementation of Xing and Niederreiter's method (Acta. Arith. 72 (1995) 281) for the construction of low-discrepancy sequences.