64 citations · 247 across the 16 of their papers we have counts for
17 papers
A Matroidal Framework for Random Access in Linear Codes
Daniella Bar-Lev, Hiram H. López, Gretchen L. Matthews +1
We study random access in linear codes when codeword symbols are sampled independently and uniformly with replacement. A code is recovery balanced if the expected number of samples…
Function Tables for Secure Distributed Matrix Multiplication
Rafael G. L. D'Oliveira, Giulia Gaggero, Arturo Jaramillo Gil +3
We introduce function tables, an entrywise representation of the coefficient functions that appear in the worker responses of a secure distributed matrix multiplication (SDMM) sche…
The permutation group of Reed-Solomon codes over arbitrary points
Eduardo Camps-Moreno, Jun Bo Lau, Hiram H. López +1
In this work, we prove that the permutation group of a Reed-Solomon code is given by the polynomials of degree one that leave the set of evaluation points invariant. Our results pr…
The Random Variables of the DNA Coverage Depth Problem
Şeyma Bodur, Stefano Lia, Hiram H. López +3
DNA data storage systems encode digital data into DNA strands, enabling dense and durable storage. Efficient data retrieval depends on coverage depth, a key performance metric. We…
Polar decreasing monomial-Cartesian codes
Eduardo Camps, Hiram H. López, Gretchen L. Matthews +1
We prove that families of polar codes with multiple kernels over certain symmetric channels can be viewed as polar decreasing monomial-Cartesian codes, offering a unified treatment…
Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes
Hiram H. López, Gretchen Matthews, Ivan Soprunov
A monomial-Cartesian code is an evaluation code defined by evaluating a set of monomials over a Cartesian product. It is a generalization of some families of codes in the literatur…
Explicit optimal-length locally repairable codes of distance 5
Allison Beemer, Ryan Coatney, Venkatesan Guruswami +2
Locally repairable codes (LRCs) have received significant recent attention as a method of designing data storage systems robust to server failure. Optimal LRCs offer the ideal trad…
Affine Cartesian codes with complementary duals
Hiram H. López, Felice Manganiello, Gretchen L. Matthews
A linear code with the property that is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesia…
Rank-Metric Codes and -Polymatroids
Elisa Gorla, Relinde Jurrius, Hiram H. López +1
This paper contributes to the study of rank-metric codes from an algebraic and combinatorial point of view. We introduce -polymatroids, the -analogue of polymatroids, and dev…
Representations of the Multicast Network Problem
Sarah E. Anderson, Wael Halbawi, Nathan Kaplan +4
We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of t…
Rank distribution of Delsarte codes
Javier de la Cruz, Elisa Gorla, Hiram H. Lopez +1
In analogy with the Singleton defect for classical codes, we propose a definition of rank defect for Delsarte rank-metric codes. We characterize codes whose rank defect and dual ra…
Projective nested cartesian codes
Cicero Carvalho, V. G. Lopez Neumann, Hiram H. Lopez
In this paper we introduce a new type of code, called projective nested cartesian code. It is obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain s…
Complete intersection vanishing ideals on degenerate tori over finite fields
Hiram H. Lopez, Rafael H. Villarreal, Leticia Zarate
We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a cor…
Computing the degree of a lattice ideal of dimension one
Hiram H. Lopez, Rafael H. Villarreal
We show that the degree of a graded lattice ideal of dimension 1 is the order of the torsion subgroup of the quotient group of the lattice. This gives an efficient method to comput…
Complete intersections in binomial and lattice ideals
Hiram H. Lopez, Rafael H. Villarreal
For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown tha…
Affine cartesian codes
Hiram H. Lopez, Carlos Renteria, Rafael H. Villarreal
We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integer…
Parameterized affine codes
Hiram H. Lopez, Eliseo Sarmiento, Maria Vaz Pinto +1
Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Groebner bases, to compute the length and the dim…