6 papers
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…
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…
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…
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…