论文标题
计算消失的图意代码理想
Computing Vanishing Ideals for Toric Codes
论文作者
论文摘要
受到错误纠正代码理论的申请的激励，我们提供了计算用于计算由$β$ graded的多项式生成的理想的生成集的方法$ \ mathbb {n}β$的$ \ mathbb {n}^d $。我们还提供了一种计算$ x $的$ \ mathbb {f} _q $合理点的消失理想的方法。 When $β=[w_1 \cdots w_r]$ is a row matrix corresponding to a numerical semigroup $\mathbb{N}β=\langle w_1,\dots,w_r \rangle$, $X$ is a weighted projective space and generators of the relevant vanishing ideal is given using generators of defining (toric) ideals of numerical semigroup rings corresponding to由$ \ {w_1，\ dots，w_r \} $的子集生成的半群。
Motivated by applications to the theory of error-correcting codes, we give methods for computing a generating set for the ideal generated by $β$-graded polynomials vanishing on certain subsets of a simplicial complete toric variety $X$ over a finite field $\mathbb{F}_q$, where $β$ is a $d\times r$ matrix whose columns generate a subsemigroup $\mathbb{N}β$ of $\mathbb{N}^d$. We also give a method for computing the vanishing ideal of the set of $\mathbb{F}_q$-rational points of $X$. When $β=[w_1 \cdots w_r]$ is a row matrix corresponding to a numerical semigroup $\mathbb{N}β=\langle w_1,\dots,w_r \rangle$, $X$ is a weighted projective space and generators of the relevant vanishing ideal is given using generators of defining (toric) ideals of numerical semigroup rings corresponding to semigroups generated by subsets of $\{w_1,\dots,w_r\}$.
