Geodesic
MacWilliams identities and matroid polynomials
The electronic journal of combinatorics, Tome 9 (2002)
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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.
DOI : 10.37236/1636
Classification : 05B35, 94B05
Mots-clés : linear code, weight enumerator 
@article{10_37236_1636,
     author = {Thomas Britz},
     title = {MacWilliams identities and matroid polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1636},
     zbl = {1038.05008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1636/}
}
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Thomas Britz. MacWilliams identities and matroid polynomials. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1636

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