We develop a new family of linear programs, that yield upper bounds on the rate of 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 improved asymptotic upper bounds on the possible rate of linear codes.
翻译:我们开发了一个由线性程序组成的新体系, 它在一定距离的代码率上产生上限。 我们的界限只适用于线性代码。 } Delsarte的LP是这个家族中最弱的一员, 我们的LP随着其控制参数的增加,其速度的上限会越来越紧。 与Delsarte相比, 数字实验显示出显著的改善。 这些令人信服的数字结果, 以及可供进行无药性分析的大量工具, 给我们带来了希望, 希望我们的工作将导致对可能线性代码率的无药性上限进行新的改进。