2025/05/15 by Şeyma Bodur, Bodur, Şeyma, Fernando Hernando +5 · 3 citations
Computer Science · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Cryptography and Data Security
paper · pdf · doi:10.48550/arxiv.2505.10068
In this work, we study the componentwise (Schur) 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.