Diego Ruano"The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval"
Comp. Appl. Math. 45, 293 (2026)
with Ş. Bodur, F. Hernando & E. Martínez-Moro
#quantumcodes #pir #csst
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https://doi.org/10.1007/s40314-026-03667-8
The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval - Computational and Applied Mathematics
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.
QIC Journal