论文标题
编码理论中的线性编程层次结构：双重解决方案
Linear Programming Hierarchies in Coding Theory: Dual Solutions
论文作者
论文摘要
速率与距离问题是编码理论中的长期开放问题。最近的论文提出了一种新的方法来解决这个问题，呼吁新的线性程序的新层次结构。如果可以找到这些LP的良好双重解决方案，这将导致对线性代码的速率与距离问题的上限提高。在这项工作中，我们在此层次结构中为LP开发了第一个双重可行解决方案。这些与广泛的参数相匹配。我们的希望是，这是迈向更好解决方案的第一步，并且在线性代码的距离问题方面改善了上限。
The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these LPs, this would result in improved upper bounds for the rate vs. distance problem of linear codes. In this work, we develop the first dual feasible solutions to the LPs in this hierarchy. These match the best-known bound for a wide range of parameters. Our hope is that this is a first step towards better solutions, and improved upper bounds for the rate vs. distance problem of linear codes.
