Name
Abstract | ||
|---|---|---|
Let G be a connected graph and let X be the set of projective points defined by the column vectors of the incidence matrix of G over a field K of any characteristic. We determine the generalized Hamming weights of the Reed–Muller-type code over the set X in terms of graph theoretic invariants. As an application to coding theory we show that if G is non-bipartite and K is a finite field of char(K)≠2, then the rth generalized Hamming weight of the linear code generated by the rows of the incidence matrix of G is the rth weak edge biparticity of G. If char(K)=2 or G is bipartite, we prove that the rth generalized Hamming weight of that code is the rth edge connectivity of G. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.disc.2019.111639 | Discrete Mathematics |
Keywords | DocType | Volume |
Incidence matrices,Edge connectivity,Generalized Hamming weights,Reed–Muller-type codes,Graphs,Weak edge biparticity | Journal | 343 |
Issue | ISSN | Citations |
1 | 0012-365X | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| José Martínez-Bernal | 1 | 0 | 1.35 |
| Miguel A. Valencia-Bucio | 2 | 0 | 0.68 |
| Rafael H. Villarreal | 3 | 75 | 15.69 |
| Valencia-Bucio Miguel A. | 4 | 0 | 0.34 |