5 papers
The permutation group of Reed-Solomon codes over arbitrary points
Eduardo Camps-Moreno, Jun Bo Lau, Hiram H. López +1
In this work, we prove that the permutation group of a Reed-Solomon code is given by the polynomials of degree one that leave the set of evaluation points invariant. Our results pr…
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…
Linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings
Daniel P. Bossaller, Hiram H. López
Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed sto…
The weight hierarchy of decreasing norm-trace codes
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +1
The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the w…
Binary Triorthogonal and CSS-T Codes for Quantum Error Correction
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +3
In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respec…