49 citations · 93 across the 18 of their papers we have counts for
21 papers
Influences of some families of error-correcting codes
Hailey Egan, Jason T. LeGrow, Gretchen L. Matthews +1
Binary codes of length may be viewed as subsets of vertices of the Boolean hypercube . The ability of a linear error-correcting code to recover erasures is connected…
Curve-lifted codes for local recovery using lines
Gretchen L. Matthews, Travis Morrison, Aidan W. Murphy
In this paper, we introduce curve-lifted codes over fields of arbitrary characteristic, inspired by Hermitian-lifted codes over . These codes are designed for loc…
Multishot Adversarial Network Decoding
Giuseppe Cotardo, Gretchen L. Matthews, Alberto Ravagnani +1
We investigate adversarial network coding and decoding focusing on the multishot regime. Errors can occur on a proper subset of the network edges and are modeled via an adversarial…
HerA Scheme: Secure Distributed Matrix Multiplication via Hermitian Codes
Roberto A. Machado, Gretchen L. Matthews, Welington Santos
We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of honest but curiou…
Relative hulls and quantum codes
Sarah E. Anderson, Eduardo Camps-Moreno, Hiram H. López +3
Given two -ary codes and , the relative hull of with respect to is the intersection . We prove that when , the relative hull dimen…
Decreasing norm-trace codes
Cícero Carvalho, Hiram H. López, Gretchen L. Matthews
The decreasing norm-trace codes are evaluation codes defined by a set of monomials closed under divisibility and the rational points of the extended norm-trace curve. In particular…
Multivariate Goppa codes
Hiram H. López, Gretchen L. Matthews
In this paper, we introduce multivariate Goppa codes, which contain as a special case the well-known, classical Goppa codes. We provide a parity check matrix for a multivariate Gop…
Explicit non-special divisors of small degree, algebraic geometric hulls, and LCD codes from Kummer extensions
Eduardo Camps, Hiram H. López, Gretchen L. Matthews
In this paper, we consider the hull of an algebraic geometry code, meaning the intersection of the code and its dual. We demonstrate how codes whose hulls are algebraic geometry co…
Erasures repair for decreasing monomial-Cartesian and augmented Reed-Muller codes of high rate
Hiram H. López, Gretchen L. Matthews, Daniel Valvo
In this work, we present linear exact repair schemes for one or two erasures in decreasing monomial-Cartesian codes DM-CC, a family of codes which provides a framework for polar co…
Codes with locality from cyclic extensions of Deligne-Lusztig curves
Gretchen L. Matthews, Fernando L. Piñero
Recently, Skabelund defined new maximal curves which are cyclic extensions of the Suzuki and Ree curves. Previously, the now well-known GK curves were found as cyclic extensions of…
Hermitian-Lifted Codes
Hiram H. López, Beth Malmskog, Gretchen L Matthews +2
In this paper, we construct codes for local recovery of erasures with high availability and constant-bounded rate from the Hermitian curve. These new codes, called Hermitian-lifted…
Triples of rational points on the Hermitian curve and their Weierstrass semigroups
Gretchen L. Matthews, Dane Skabelund, Michael Wills
In this paper, we study configurations of three rational points on the Hermitian curve over and classify them according to their Weierstrass semigroups. For $q>3…
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…
On Laplacian Monopoles
Cong X. Kang, Gretchen L. Matthews, Justin D. Peachey
We consider the action of the (combinatorial) Laplacian of a finite and simple graph on integer vectors. By a \emph{Laplacian monopole} we mean an image vector negative at exactly…
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…
Service Rate Region of Content Access from Erasure Coded Storage
Sarah Anderson, Ann Johnston, Gauri Joshi +3
We consider storage systems in which files are stored over nodes. A node may be systematic for a particular file in the sense that access to it gives access to the file. Al…
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…
On the Service Capacity Region of Accessing Erasure Coded Content
Mehmet Aktas, Sarah E. Anderson, Ann Johnston +5
Cloud storage systems generally add redundancy in storing content files such that files are replicated or erasure coded and stored on nodes. In addition to providing re…
Locally recoverable codes from algebraic curves and surfaces
Alexander Barg, Kathryn Haymaker, Everett W. Howe +2
A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other c…
Locally Recoverable Codes with Availability from Fiber Products of Curves
Kathryn Haymaker, Beth Malmskog, Gretchen Matthews
We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vlăduţ to those with arbitrarily many recovery sets by exploiting the struct…
Codes for distributed storage from 3-regular graphs
Shuhong Gao, Fiona Knoll, Felice Manganiello +1
This paper considers distributed storage systems (DSSs) from a graph theoretic perspective. A DSS is constructed by means of the path decomposition of a 3- regular graph into P4 pa…