3 papers
cs.IT2024
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,…
cs.IT2024
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…
cs.IT2024
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…