## 5 Citations

### Free Resolutions and Generalized Hamming Weights of binary linear codes

- Computer Science, MathematicsMathematics
- 2022

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

- Computer Science, Mathematics
- 2022

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

- MathematicsDesigns, Codes and Cryptography
- 2021

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

- MathematicsArXiv
- 2021

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.

## References

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### A generalization of weight polynomials to matroids

- MathematicsDiscret. Math.
- 2016

### Graded Betti numbers of Cohen–Macaulay modules and the multiplicity conjecture

- Mathematics
- 2008

We give conjectures on the possible graded Betti numbers of Cohen–Macaulay modules up to multiplication by positive rational numbers. The idea is that the Betti diagrams should be non‐negative linear…

### The Geometry of Two‐Weight Codes

- Mathematics
- 1986

On etudie les relations entre les codes [n,k] lineaires a deux poids, les ensembles (n,k,h 1 h 2 ) projectifs et certains graphes fortement reguliers

### Hermitian Varieties in a Finite Projective Space PG(N, q 2)

- MathematicsCanadian Journal of Mathematics
- 1966

The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another…

### Hamming weights and Betti numbers of Stanley–Reisner rings associated to matroids

- MathematicsApplicable Algebra in Engineering, Communication and Computing
- 2012

This work shows how the weights of a matroid M are determined by the Stanley–Reisner ring of the simplicial complex whose faces are the independent sets of $$M$$, and derives some consequences.

### Cohen-Macaulay Complexes

- Mathematics
- 1977

Let Δ be a finite simplicial complex (or complex for short) on the vertex set V = (x1,…,xn). Thus, Δ is a collection of subsets of V satisfying the two conditions: (i) (xi) e Δ for all xi e V, and…

### On the bettinumbers of finite pure and linear resolutions

- Mathematics
- 1984

A characterization in terms of the Bettinumbers for a module possessing a pure resolution to be Cohen-Macauiay is given, the conjecture that the Bettinumbers should satisfy is being proven roi the…