{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T18:33:46Z","timestamp":1773340426744,"version":"3.50.1"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:00:00Z","timestamp":1773273600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:00:00Z","timestamp":1773273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2026,4]]},"abstract":"Abstract<\/jats:title>\n \n A strong\n s<\/jats:italic>\n -blocking set in a projective space is a set of points that intersects each codimension-\n s<\/jats:italic>\n subspace in a spanning set of the subspace. We present an explicit construction of such sets in a\n \n \n $$(k - 1)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n k<\/mml:mi>\n -<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -dimensional projective space over\n \n \n $$\\mathbb {F}_q$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n q<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of size\n \n \n $$O_s(q^s k)$$<\/jats:tex-math>\n \n \n \n O<\/mml:mi>\n s<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n \n q<\/mml:mi>\n s<\/mml:mi>\n <\/mml:msup>\n k<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , which is optimal up to the constant factor depending on\n s<\/jats:italic>\n . This also yields an optimal explicit construction of affine blocking sets in\n \n \n $$\\mathbb {F}_q^k$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n q<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msubsup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n with respect to codimension-\n \n \n $$(s+1)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n s<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n affine subspaces, and of\n s<\/jats:italic>\n -minimal codes. Our approach is motivated by a recent construction of Alon, Bishnoi, Das, and Neri of strong 1-blocking sets, which uses expander graphs with a carefully chosen set of vectors as their vertex set. The main novelty of our work lies in constructing specific hypergraphs on top of these expander graphs, where tree-like configurations correspond to strong\n s<\/jats:italic>\n -blocking sets. We also discuss some connections to size-Ramsey numbers of hypergraphs, which might be of independent interest.\n <\/jats:p>","DOI":"10.1007\/s00493-026-00202-5","type":"journal-article","created":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T08:43:35Z","timestamp":1773305015000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Explicit Constructions of Optimal Blocking Sets and Minimal Codes"],"prefix":"10.1007","volume":"46","author":[{"given":"Anurag","family":"Bishnoi","sequence":"first","affiliation":[]},{"given":"Istv\u00e1n","family":"Tomon","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,3,12]]},"reference":[{"issue":"1","key":"202_CR1","doi-asserted-by":"publisher","first-page":"115","DOI":"10.3934\/amc.2020104","volume":"16","author":"GN Alfarano","year":"2022","unstructured":"Alfarano, G.N., Borello, M., Neri, A.: A geometric characterization of minimal codes and their asymptotic performance. 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