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Appl. Math."],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    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\n                    <jats:italic>J<\/jats:italic>\n                    -affine variety codes are well suited for such products, generalizing earlier results for cyclic, Reed\u2013Muller, hyperbolic, and toric codes. Using this correspondence, we construct CSS-T quantum codes from weighted Reed\u2013Muller codes and from binary subfield-subcodes of\n                    <jats:italic>J<\/jats:italic>\n                    -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\n                    <jats:italic>J<\/jats:italic>\n                    -affine variety codes, and show that they outperform existing PIR schemes.\n                  <\/jats:p>","DOI":"10.1007\/s40314-026-03667-8","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T06:42:22Z","timestamp":1773124942000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6171-7975","authenticated-orcid":false,"given":"\u015eeyma","family":"Bodur","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9758-2152","authenticated-orcid":false,"given":"Fernando","family":"Hernando","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1243-2049","authenticated-orcid":false,"given":"Edgar","family":"Mart\u00ednez-Moro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7304-0087","authenticated-orcid":false,"given":"Diego","family":"Ruano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,10]]},"reference":[{"issue":"3","key":"3667_CR1","doi-asserted-by":"publisher","first-page":"1945","DOI":"10.1109\/TIT.2018.2791994","volume":"64","author":"K Banawan","year":"2018","unstructured":"Banawan K, Ulukus S (2018) The capacity of private information retrieval from coded databases. 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