Abstract
We present generalisations of several MacWilliams type identities, including those by Kløve and Shiromoto, and of the theorems of Greene and Barg that describe how the Tutte polynomial of the vector matroid of a linear code determines the $r$th support weight enumerators of the code. One of our main tools is a generalisation of a decomposition theorem due to Brylawski.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Linear codes over signed graphs;Designs, Codes and Cryptography;2019-10-09
2. MacWilliams Identities for $m$-tuple Weight Enumerators;SIAM Journal on Discrete Mathematics;2014-01
3. Demi-matroids from codes over finite Frobenius rings;Designs, Codes and Cryptography;2013-11-10
4. A MacWilliams type identity for matroids;Discrete Mathematics;2008-10
5. Higher support matroids;Discrete Mathematics;2007-08