49 citations · 54 across the 7 of their papers we have counts for
8 papers
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…
Parity-check Codes from Disjunct Matrices
Kathryn Haymaker, Emily McMillon
The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct m…
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…
Spectral Radii of Arithmetical Structures on Cycle Graphs
Alexander Diaz-Lopez, Kathryn Haymaker, Michael Tait
Let be a finite, connected graph. An arithmetical structure on is a pair of positive integer-valued vectors such that $(\text{diag}(\mathbf{d})-A_…
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…
The graph structure of graph groups that are subgroups of Thompson's group
Nathan Corwin, Kathryn Haymaker
We determine exactly which graph products, also known as Right Angled Artin Groups, embed into Richard Thompson's group . It was shown by Bleak and Salazar-Diaz that $\mathbb{Z}…
Geometric WOM codes and coding strategies for multilevel flash memories
Kathryn Haymaker, Christine A. Kelley
This paper investigates the design and application of write-once memory (WOM) codes for flash memory storage. Using ideas from Merkx ('84), we present a construction of WOM codes b…