6 papers
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, YaÄmur ÃakıroÄlu, 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-DÃaz, Umberto MartÃnez-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…
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…