Pure Resolutions, Linear Codes, and Betti Numbers

@article{Ghorpade2020PureRL,
  title={Pure Resolutions, Linear Codes, and Betti Numbers},
  author={Sudhir R. Ghorpade and Prasant Singh},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.01799}
}
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5 Citations
Background Citations
1

5 Citations

Some matroids related to sum-rank metric codes

Free Resolutions and Generalized Hamming Weights of binary linear codes

It is proved that the first and second generalized Hamming weights of a binary linear code can be computed from a set of monomials associated with a binomial ideal related with the code.

Generalized weights of codes over rings and invariants of monomial ideals

An algebraic theory of supports for R-linear codes of fixed length, where R is a finite commutative unitary ring, states that the generalized weights of a code can be obtained from the graded Betti numbers of its associated monomial ideal.

Möbius and coboundary polynomials for matroids

It is explained how the connection with these Stanley–Reisner rings forces the coefficients of the two-variable coboundary polynomials and Möbius polynomers to satisfy certain universal equations.

On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes

A complete characterization of the purity of graded minimal free resolutions of StanleyReisner rings associated to generalized Reed-Muller codes of an arbitrary order is given.

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