论文标题
分隔曲线上的Riemann-Roch空间的明确基础
Explicit bases of the Riemann-Roch spaces on divisors on hyperelliptic curves
论文作者
论文摘要
对于（假想的）高椭圆曲线$ \ Mathcal {H} $属$ g $，我们确定Riemann-Roch空间的基础G $，$ω$是一个Weierstrass点，是无穷大的点。作为一个应用程序，我们确定$ j = g = 3 $和$ n = 4的GOPPA代码的发电机矩阵。
For an (imaginary) hyperelliptic curve $\mathcal{H}$ of genus $g$, we determine a basis of the Riemann-Roch space $\mathcal{L}(D)$, where $D$ is a divisor with positive degree $n$, linearly equivalent to $P_1+\cdots+ P_j+(n-j)Ω$, with $0 \le j \le g$, where $Ω$ is a Weierstrass point, taken as the point at infinity. As an application, we determine a generator matrix of a Goppa code for $j=g=3$ and $n=4.$
