论文标题
线性代码的速率vs.-distance问题中的新的LP上限
New LP-based Upper Bounds in the Rate-vs.-Distance Problem for Linear Codes
论文作者
论文摘要
我们开发了一个新的线性程序系列，该系列的上限在给定距离的二进制线性代码速率上产生上限。我们的边界仅适用于线性代码。} delsarte的LP是该家族中最弱的成员，随着其控制参数的增加，我们的LP在速率上的上限越来越紧。与Delsarte相比，数值实验显示出显着改善。这些令人信服的数值结果以及可用于渐近分析的各种工具，使我们希望我们的工作将导致新的和改进的渐近上限，以实可能的线性代码速率。 Coregliano，Jeronimo和Jones的同时工作提供了一个密切相关的线性程序系列，这些系列与真实的界限相聚。在这里，我们为同一LP提供了新的融合证明。
We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields increasingly tighter upper bounds on the rate as its control parameter increases. Numerical experiments show significant improvement compared to Delsarte. These convincing numerical results, and the large variety of tools available for asymptotic analysis, give us hope that our work will lead to new and improved asymptotic upper bounds on the possible rate of linear codes. A concurrent work by Coregliano, Jeronimo, and Jones offers a closely related family of linear programs which converges to the true bound. Here we provide a new proof of convergence for the same LPs.
