Extensions of the Critical Theorem
Extensions of the Critical Theorem
复制标题
临界定理的扩展
DOI：
10.1016/j.disc.2005.10.002
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Thomas Britz
中科院分区：
文献类型：
--
作者：
Thomas Britz
临界定理，由于亨利克拉波和吉安-卡洛罗塔，以前已扩大或推广，在许多不同的方式。本文的主要结果是一个一般形式的临界定理，其中包括许多这些结果。应用程序包括概括的一个定理柯蒂斯格林，描述了如何重量枚举的线性代码是由Tutte多项式的相关向量拟阵，以及概括的MacWilliams身份的线性代码。
The Critical Theorem, due to Henry Crapo and Gian-Carlo Rota, has previously been extended or generalised in a number of different ways. The main result of the present paper is a general form of the Critical Theorem that encompasses many of these results. Applications include generalisations of a theorem by Curtis Greene that describes how the weight enumerator of a linear code is determined by the Tutte polynomial of the associated vector matroid, as well as generalisations of the MacWilliams identity for linear codes.