RT info:eu-repo/semantics/article
T1 The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval
A1 Bodur, Seyma
A1 Hernando, Fernando
A1 Martínez Moro, Edgar
A1 Ruano Benito, Diego
K1 Teoría de la información
K1 Computación cuántica
K1 Álgebra
K1 Producto de Schur
K1 Recuperación de información privada
K1 Códigos cuánticos CSS-T
K1 1201 Álgebra
K1 1203 Ciencia de Los Ordenadores
AB In this work, we study the Schur (componentwise) product of monomial-Cartesian codes by exploiting its correspondence with the Minkowski sum of their defining exponent sets. We show that J-affine variety codes are well suited for such products, generalizing earlier results for cyclic, Reed–Muller, hyperbolic, and toric codes. Using this correspondence, we construct CSS-T quantum codes from weighted Reed–Muller codes and from binary subfield-subcodes of J-affine variety codes, leading to codes with better parameters than previously known. Finally, we present Private Information Retrieval (PIR) constructions for multiple colluding servers based on hyperbolic codes and subfield-subcodes of J-affine variety codes, and show that they outperform existing PIR schemes.
PB Springer Nature
SN 1807-0302
YR 2026
FD 2026
LK https://uvadoc.uva.es/handle/10324/83387
UL https://uvadoc.uva.es/handle/10324/83387
LA eng
NO Computational and Applied Mathematics, 2026, vol. 45, n. 8.
NO Producción Científica
DS UVaDOC
RD 10-mar-2026