Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids
arXiv:1108.3172 · doi:10.1007/s00200-012-0183-7
Abstract
To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid.
Cited by in corpus (6)
- Generalized Hamming weights for almost affine codes
- A generalization of weight polynomials to matroids
- Pure Resolutions, Linear Codes, and Betti Numbers
- Indicator functions, v-numbers and Gorenstein rings in the theory of projective Reed-Muller-type codes
- Betti numbers associated to the facet ideal of a matroid
- Betti numbers of skeletons