{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T13:15:03Z","timestamp":1777295703810,"version":"3.51.4"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Anusandhan National Research Foundation (ANRF), Government of India","award":["CRG\/2022\/000344"],"award-info":[{"award-number":["CRG\/2022\/000344"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1007\/s10623-026-01803-3","type":"journal-article","created":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T12:01:05Z","timestamp":1775563265000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Binary code generated by the hyperbolic quadrics of $$W(2n-1,q),$$ q even"],"prefix":"10.1007","volume":"94","author":[{"given":"Devjyoti","family":"Das","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bart","family":"De Bruyn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binod Kumar","family":"Sahoo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N. S. Narasimha","family":"Sastry","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,7]]},"reference":[{"key":"1803_CR1","volume-title":"Some Topics in Finite Geometrical Structures. Institute of Statistics Mimeo Series No. 439","author":"A Barlotti","year":"1965","unstructured":"Barlotti A.: Some Topics in Finite Geometrical Structures. Institute of Statistics Mimeo Series No. 439. University of North Carolina, Chapel Hill (1965)."},{"key":"1803_CR2","doi-asserted-by":"crossref","unstructured":"Biondi P., Lo Re P.M., Storme L.: On minimum size blocking sets of external lines to a quadric in $${\\rm PG}(3, q)$$. Beitr\u00e4ge Algebra Geom. 48(1), 209\u2013215 (2007).","DOI":"10.2140\/iig.2007.5.1"},{"key":"1803_CR3","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/S0021-9800(66)80007-8","volume":"1","author":"RC Bose","year":"1966","unstructured":"Bose R.C., Burton R.C.: A characterization of flat spaces in a finite geometry and the uniqueness of the Hamming and the MacDonald codes. J. Comb. Theory 1, 96\u2013104 (1966).","journal-title":"J. Comb. Theory"},{"issue":"1","key":"1803_CR4","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/BF00181468","volume":"36","author":"AE Brouwer","year":"1990","unstructured":"Brouwer A.E., Wilbrink H.A.: Ovoids and fans in the generalized quadrangle $$Q(4,2)$$. Geom. Dedic. 36(1), 121\u2013124 (1990).","journal-title":"Geom. Dedic."},{"key":"1803_CR5","doi-asserted-by":"crossref","unstructured":"De Bruyn B.: Two new classes of hyperplanes of the dual polar space DH( 2n -\u2212 1, 4) not arising from the Grassmann embedding. Linear Algebra Appl. 429(8\u20139), 2030\u20132045 (2008).","DOI":"10.1016\/j.laa.2008.05.036"},{"issue":"6","key":"1803_CR6","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1080\/03081080802012623","volume":"57","author":"B De Bruyn","year":"2009","unstructured":"De Bruyn B., Pasini A.: On symplectic polar spaces over non-perfect fields of characteristic 2. Linear Multilinear Algebra 57(6), 567\u2013575 (2009).","journal-title":"Linear Multilinear Algebra"},{"issue":"6","key":"1803_CR7","doi-asserted-by":"publisher","first-page":"1739","DOI":"10.1007\/s10623-024-01559-8","volume":"93","author":"B De Bruyn","year":"2025","unstructured":"De Bruyn B., Pradhan P., Sahoo B.K.: Blocking sets of secant and tangent lines with respect to a quadric of $${\\rm PG}(n, q)$$. Des. Codes Cryptogr. 93(6), 1739\u20131760 (2025).","journal-title":"Des. Codes Cryptogr."},{"issue":"1","key":"1803_CR8","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1016\/0021-8693(79)90157-1","volume":"59","author":"RH Dye","year":"1979","unstructured":"Dye R.H.: Interrelations of symplectic and orthogonal groups in characteristic two. J. Algebra 59(1), 202\u2013221 (1979).","journal-title":"J. Algebra"},{"key":"1803_CR9","first-page":"170","volume":"32","author":"G Fellegara","year":"1962","unstructured":"Fellegara G.: Gli ovaloidi in uno spazio tridimensionale di Galois di ordine 8. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 32, 170\u2013176 (1962).","journal-title":"Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat."},{"key":"1803_CR10","series-title":"Oxford Mathematical Monographs","volume-title":"Finite Projective Spaces of Three Dimensions","author":"JWP Hirschfeld","year":"1985","unstructured":"Hirschfeld J.W.P.: Finite Projective Spaces of Three Dimensions. Oxford Mathematical Monographs. Oxford University Press, New York (1985)."},{"key":"1803_CR11","doi-asserted-by":"crossref","unstructured":"Hirschfeld J.W.P.: Projective Geometries over Finite Fields, 2nd edn. Oxford Mathematical Monographs. Oxford University Press, New York (1998).","DOI":"10.1093\/oso\/9780198502951.001.0001"},{"key":"1803_CR12","series-title":"Springer Monographs in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-6790-7","volume-title":"General Galois Geometries","author":"JWP Hirschfeld","year":"2016","unstructured":"Hirschfeld J.W.P., Thas J.A.: General Galois Geometries. Springer Monographs in Mathematics. Springer, London (2016)."},{"key":"1803_CR13","doi-asserted-by":"crossref","unstructured":"Metsch K.: Bose-Burton type theorems for finite projective, affine and polar spaces. London Mathematical Society Lecture Note Series. vol. 267, pp. 137\u2013166. Cambridge University Press, Cambridge (1999).","DOI":"10.1017\/CBO9780511721335.006"},{"issue":"1\u20132","key":"1803_CR14","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF01222898","volume":"38","author":"CM O\u2019Keefe","year":"1990","unstructured":"O\u2019Keefe C.M., Penttila T.: Ovoids of $${\\rm PG}(3,16)$$ are elliptic quadrics. J. Geom. 38(1\u20132), 95\u2013106 (1990).","journal-title":"J. Geom."},{"issue":"1\u20132","key":"1803_CR15","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1007\/BF01228289","volume":"44","author":"CM O\u2019Keefe","year":"1992","unstructured":"O\u2019Keefe C.M., Penttila T.: Ovoids of $${\\rm PG}(3,16)$$ are elliptic quadrics. II. J. Geom. 44(1\u20132), 140\u2013159 (1992).","journal-title":"J. Geom."},{"issue":"1\u20132","key":"1803_CR16","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/BF01222671","volume":"50","author":"CM O\u2019Keefe","year":"1994","unstructured":"O\u2019Keefe C.M., Penttila T., Royle G.F.: Classification of ovoids in $${\\rm PG}(3,32)$$. J. Geom. 50(1\u20132), 143\u2013150 (1994).","journal-title":"J. Geom."},{"key":"1803_CR17","doi-asserted-by":"crossref","unstructured":"Payne S.E., Thas J.A.: Finite Generalized Quadrangles, 2nd edn. EMS Series of Lectures in Mathematics. European Mathematical Society (EMS), Z$$\\ddot{\\text{u}}$$rich (2009).","DOI":"10.4171\/066"},{"issue":"3","key":"1803_CR18","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1007\/s10623-022-01014-6","volume":"90","author":"T Penttila","year":"2022","unstructured":"Penttila T.: Uniqueness of the inversive plane of order sixty-four. Des. Codes Cryptogr. 90(3), 827\u2013834 (2022).","journal-title":"Des. Codes Cryptogr."},{"issue":"4","key":"1803_CR19","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1515\/advgeom-2018-0009","volume":"19","author":"BK Sahoo","year":"2019","unstructured":"Sahoo B.K., Sahu B.: Blocking sets of certain line sets related to a hyperbolic quadric in $${\\rm PG}(3, q)$$. Adv. Geom. 19(4), 477\u2013486 (2019).","journal-title":"Adv. Geom."},{"issue":"1","key":"1803_CR20","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s10623-015-0040-3","volume":"79","author":"BK Sahoo","year":"2016","unstructured":"Sahoo B.K., Sastry N.S.N.: Binary codes of the symplectic generalized quadrangle of even order. Des. Codes Cryptogr. 79(1), 163\u2013170 (2016).","journal-title":"Des. Codes Cryptogr."},{"issue":"1","key":"1803_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jcta.2000.3118","volume":"94","author":"NSN Sastry","year":"2001","unstructured":"Sastry N.S.N., Sin P.: Codes associated with nondegenerate quadrics of a symplectic space of even order. J. Comb. Theory Ser. A 94(1), 1\u201314 (2001).","journal-title":"J. Comb. Theory Ser. A"},{"issue":"3","key":"1803_CR22","first-page":"5","volume":"2","author":"J Schillewaert","year":"2022","unstructured":"Schillewaert J., Van de Voorde G.: Quasi-polar spaces. Comb. Theory 2(3), 5 (2022).","journal-title":"Comb. Theory"},{"key":"1803_CR23","unstructured":"Tallini G.: Fibrations through lines in a nonsingular quadric $$Q_{4,q}$$ of $${\\rm PG}(4,q)$$. Atti Accad. Peloritana Pericolanti. Cl. Sci. Fis. Mat. Natur. 66, 127\u2013146 (1988)."},{"key":"1803_CR24","series-title":"Sigma Series in Pure Mathematics","volume-title":"The Geometry of the Classical Groups","author":"DE Taylor","year":"1992","unstructured":"Taylor D.E.: The Geometry of the Classical Groups, vol. 9. Sigma Series in Pure Mathematics. Heldermann Verlag, Berlin (1992)."},{"issue":"1\u20134","key":"1803_CR25","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/BF01447417","volume":"10","author":"JA Thas","year":"1981","unstructured":"Thas J.A.: Ovoids and spreads of finite classical polar spaces. Geom. Dedic. 10(1\u20134), 135\u2013143 (1981).","journal-title":"Geom. Dedic."},{"key":"1803_CR26","series-title":"Springer Monographs in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20972-7","volume-title":"Foundations of Incidence Geometry: Projective and Polar Spaces","author":"J Ueberberg","year":"2011","unstructured":"Ueberberg J.: Foundations of Incidence Geometry: Projective and Polar Spaces. Springer Monographs in Mathematics. Springer, Heidelberg (2011)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01803-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-026-01803-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01803-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T12:15:47Z","timestamp":1777292147000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-026-01803-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["1803"],"URL":"https:\/\/doi.org\/10.1007\/s10623-026-01803-3","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"19 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"79"}}