9 citations · 10 across the 12 of their papers we have counts for
13 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…
Digital signature schemes based on code equivalence and syndrome decoding from restricted errors
Sarah Arpin, Jason T. LeGrow, Hiram H. López +1
Digital signature schemes are an important cryptographic tool to ensure data authenticity and integrity in many applications that must be resilient to attacks, including those faci…
Weierstrass semigroups and the order bound
Alix Barraud, Yağmur Çakıroğlu, Bianca Gouthier +2
The aim of this survey is to provide the reader with an essential and accessible introduction to the theory of Weierstrass semigroups, in the context of the theory developed by K.-…
Transversal gates for quantum CSS codes
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +2
In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of…
A repair scheme for a distributed storage system based on multivariate polynomials
Hiram H. López, Gretchen L. Matthews, Daniel Valvo
A distributed storage system stores data across multiple nodes, with the primary objective of enabling efficient data recovery even in the event of node failures. The main goal of…
The Clifford defect of a numerical semigroup
Eduardo Camps-Moreno, Adrián Fidalgo-Díaz, Umberto Martínez-Peñas +1
The Clifford defect is a rational number associated to the Weierstrass semigroup at a given point of an algebraic curve. It describes the error-correcting capability of the so-call…
The weight hierarchy of decreasing norm-trace codes
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +1
The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the w…
Binary Triorthogonal and CSS-T Codes for Quantum Error Correction
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +3
In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respec…
Toward Quantum CSS-T Codes from Sparse Matrices
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +1
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a pair of binary linear codes and…
Fractional decoding of algebraic geometry codes over extension fields
Eduardo Camps-Moreno, Gretchen L. Matthews, Welington Santos
In this paper, we study algebraic geometry codes from curves over through their virtual projections which are algebraic geometric codes over . W…
An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +3
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1,…
Mathematical LoRE: Local Recovery of Erasures using Polynomials, Curves, Surfaces, and Liftings
Kathryn Haymaker, Hiram H. López, Beth Malmskog +2
Employing underlying geometric and algebraic structures allows for constructing bespoke codes for local recovery of erasures. We survey techniques for enriching classical codes wit…
Algebraic hierarchical locally recoverable codes with nested affine subspace recovery
Kathryn Haymaker, Beth Malmskog, Gretchen L. Matthews
Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. These subsets are typically of small cardina…