## 10 Citations

### Generalized star configurations and the Tutte polynomial

- MathematicsArXiv
- 2016

The degree of a generalized star configuration as a projective scheme is determined by the Tutte polynomial of the code, and preliminary results on the primary decomposition of the defining ideals of these schemes are obtained.

### Generalized star configurations and the Tutte polynomial

- MathematicsJournal of Algebraic Combinatorics
- 2017

From the generating matrix of a linear code, one can construct a sequence of generalized star configurations which are strongly connected to the generalized Hamming weights and the underlying matroid…

### 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.

### Steiner systems and configurations of points

- MathematicsDesigns, Codes and Cryptography
- 2020

The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System S(t, n, v) we associate two ideals, in a…

### Fat points, partial intersections and Hamming distance

- MathematicsJournal of Algebra and Its Applications
- 2019

We use two main techniques, namely, residuation and separators of points, to show that the Hilbert function of a certain fat point set supported on a grid complete intersection is the same as the…

### Homological properties of ideals generated by $a$-fold products of linear forms

- Mathematics
- 2019

Let $\Sigma$ be a finite collection of linear forms in $\mathbb K[x_0,\ldots,x_n]$, where $\mathbb K$ is a field. Let $1\leq a\leq |\Sigma|$. In this article we prove the conjecture that the ideal…

### On ideals generated by a-fold products of linear forms

- MathematicsJournal of Commutative Algebra
- 2021

Let $\mathbb K$ be a field of characteristic 0. Given $n$ linear forms in $R=\mathbb K[x_1,\ldots,x_k]$, with no two proportional, in one of our main results we show that the ideal $I\subset R$…

### Equivalent matrices up to permutations

- Computer Science, Mathematics
- 2018

By using codewords of minimum weight of a linear code, in concordance with a couple of methods to solve the matrix equation XA=BY, this work presents an efficient way to determine the entire encryption keys for the McEliece cryptosystems built on Reed-Solomon codes.

### On the Geramita-Harbourne-Migliore conjecture

- MathematicsTransactions of the American Mathematical Society
- 2019

Let $\Sigma$ be a finite collection of linear forms in $\mathbb K[x_0,\ldots,x_n]$, where $\mathbb K$ is a field. Denote ${\rm Supp}(\Sigma)$ to be the set of all nonproportional elements of…

### Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements

- Materials ScienceJournal of Algebraic Combinatorics
- 2020

We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane and give a number of applications. First, we prove…

## References

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- Computer ScienceApplicable Algebra in Engineering, Communication and Computing
- 2009

This note shows that the methods used to find a lower bound for the minimal distance of complete intersection evaluation codes should apply to the case of (arithmetically) Gorenstein evaluation codes, and studies other lower bounds on the minimal Distance coming from the syzygies.

### Algebras Generated by Reciprocals of Linear Forms

- Mathematics
- 2001

Let Δ be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C(Δ) of rational functions generated by {1/α ∣ α ∈ Δ}.…

### Codes, arrangements and matroids

- Mathematics
- 2013

This chapter treats error-correcting codes and their weight enumerator as the center of several closely related topics such as arrangements of hyperplanes, graph theory, matroids, posets and…

### Bounding invariants of fat points using a coding theory construction

- Mathematics, Computer Science
- 2011

### Commutative algebras for arrangements

- MathematicsNagoya Mathematical Journal
- 1994

Let V be a vector space of dimension l over some field K. A hyperplane H is a vector subspace of codimension one. An arrangement is a finite collection of hyperplanes in V. We use [7] as a general…

### Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement

- Mathematics
- 2012

Let A be a collection of n linear hyperplanes in k^l, where k is an algebraically closed field. The Orlik-Terao algebra of A is the subalgebra R(A) of the rational functions generated by reciprocals…

### Algebraic geometry modeling in information theory

- Computer Science
- 2013

Sage: A Basic Overview for Coding Theory and Cryptography (D Joyner) Aspects of Random Network Coding (O Geil and C Thomsen) Steganography from a Coding Theory Point of View (C Munuera) An…

### 1 1 M ay 2 00 1 Algebras generated by reciprocals of linear forms

- Mathematics
- 2008

Let ∆ be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C(∆) of rational functions generated by {1/α | α ∈ ∆}.…