论文标题
识别和实现电感刺穿的代码
Recognizing and Realizing Inductively Pierced Codes
论文作者
论文摘要
我们证明了一类电感刺穿的代码类别的代数和组合表征，从而解决了毛，肥胖和扬尔斯的猜想。从一个名为其规范形式的代码的代数不变开始，我们解释了如何在多项式时间内计算穿孔顺序（如果存在）。给定代码的穿刺顺序，我们说明了如何使用良好的开放球集合来构建代码的实现，并对存在这种实现的最小维度进行分类。
We prove algebraic and combinatorial characterizations of the class of inductively pierced codes, resolving a conjecture of Gross, Obatake, and Youngs. Starting from an algebraic invariant of a code called its canonical form, we explain how to compute a piercing order in polynomial time, if one exists. Given a piercing order of a code, we explain how to construct a realization of the code using a well-formed collection of open balls, and classify the minimal dimension in which such a realization exists.
