{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T00:02:57Z","timestamp":1769299377913,"version":"3.49.0"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T00:00:00Z","timestamp":1630022400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T00:00:00Z","timestamp":1630022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"italian national group for algebraic and geometric structures and their applications","award":["U-UFMBAZ-2019-000160"],"award-info":[{"award-number":["U-UFMBAZ-2019-000160"]}]},{"name":"italian national group for algebraic and geometric structures and their applications","award":["11.02.2019"],"award-info":[{"award-number":["11.02.2019"]}]},{"name":"italian national group for algebraic and geometric structures and their applications","award":["U-UFMBAZ-2019-000160"],"award-info":[{"award-number":["U-UFMBAZ-2019-000160"]}]},{"name":"italian national group for algebraic and geometric structures and their applications","award":["11.02.2019"],"award-info":[{"award-number":["11.02.2019"]}]},{"DOI":"10.13039\/501100010607","name":"university of perugia","doi-asserted-by":"crossref","award":["Project No. 98751: Strutture Geometriche"],"award-info":[{"award-number":["Project No. 98751: Strutture Geometriche"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010607","name":"university of perugia","doi-asserted-by":"crossref","award":["Combinatoria e loro Applicazioni"],"award-info":[{"award-number":["Combinatoria e loro Applicazioni"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010607","name":"university of perugia","doi-asserted-by":"crossref","award":["Base Research Fund 2017-2019"],"award-info":[{"award-number":["Base Research Fund 2017-2019"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010607","name":"university of perugia","doi-asserted-by":"crossref","award":["Project No. 98751: Strutture Geometriche"],"award-info":[{"award-number":["Project No. 98751: Strutture Geometriche"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010607","name":"university of perugia","doi-asserted-by":"crossref","award":["Combinatoria e loro Applicazioni"],"award-info":[{"award-number":["Combinatoria e loro Applicazioni"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010607","name":"university of perugia","doi-asserted-by":"crossref","award":["Base Research Fund 2017-2019"],"award-info":[{"award-number":["Base Research Fund 2017-2019"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s10623-021-00911-6","type":"journal-article","created":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T15:06:56Z","timestamp":1630076816000},"page":"2211-2233","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Twisted cubic and point-line incidence matrix in $$\\mathrm {PG}(3,q)$$"],"prefix":"10.1007","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5827-4560","authenticated-orcid":false,"given":"Alexander A.","family":"Davydov","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7961-0260","authenticated-orcid":false,"given":"Stefano","family":"Marcugini","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5476-5365","authenticated-orcid":false,"given":"Fernanda","family":"Pambianco","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,27]]},"reference":[{"issue":"1\/2","key":"911_CR1","first-page":"133","volume":"6","author":"S Ball","year":"2019","unstructured":"Ball S., Lavrauw M.: Arcs in finite projective spaces. EMS Surv. Math. Sci. 6(1\/2), 133\u2013172 (2019).","journal-title":"EMS Surv. Math. Sci."},{"issue":"1","key":"911_CR2","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1109\/TIT.2005.860415","volume":"52","author":"A Barg","year":"2006","unstructured":"Barg A., Zemor G.: Distances properties of expander codes. IEEE Trans. Inf. Theory 52(1), 78\u201390 (2006).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"911_CR3","doi-asserted-by":"publisher","first-page":"101710","DOI":"10.1016\/j.ffa.2020.101710","volume":"67","author":"D Bartoli","year":"2020","unstructured":"Bartoli D., Davydov A.A., Marcugini S., Pambianco F.: On planes through points off the twisted cubic in PG(3, q) and multiple covering codes. Finite Fields Appl. 67, 101710 (2020).","journal-title":"Finite Fields Appl."},{"key":"911_CR4","doi-asserted-by":"crossref","unstructured":"Blokhuis A., Pellikaan R., Sz\u00f6nyi T.: The extended coset leader weight enumerator of a twisted cubic code, arXiv:2103.16904 [math.CO] (2021).","DOI":"10.1007\/s10623-022-01060-0"},{"key":"911_CR5","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.disc.2005.03.010","volume":"296","author":"G Bonoli","year":"2005","unstructured":"Bonoli G., Polverino O.: The twisted cubic in PG(3, q) and translation spreads in $$H(q)$$. Discret. Math. 296, 129\u2013142 (2005).","journal-title":"Discret. Math."},{"key":"911_CR6","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma W., Cannon J., Playoust C.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24, 235\u2013265 (1997).","journal-title":"J. Symbolic Comput."},{"key":"911_CR7","first-page":"495","volume":"6","author":"AA Bruen","year":"1977","unstructured":"Bruen A.A., Hirschfeld J.W.P.: Applications of line geometry over finite fields I: The twisted cubic. Geom. Dedicata 6, 495\u2013509 (1977).","journal-title":"Geom. Dedicata"},{"key":"911_CR8","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1006\/eujc.2001.0578","volume":"23","author":"I Cardinali","year":"2002","unstructured":"Cardinali I., Lunardon G., Polverino O., Trombetti R.: Spreads in $$H(q)$$ and 1-systems of $$Q(6, q)$$. Eur. J. Combin. 23, 367\u2013376 (2002).","journal-title":"Eur. J. Combin."},{"key":"911_CR9","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/BF00147659","volume":"13","author":"LRA Casse","year":"1982","unstructured":"Casse L.R.A., Glynn D.G.: The solution to Beniamino Segre\u2019s problem $$I_{r, q}$$, $$r = 3$$, $$q = 2^h$$. Geom. Dedicata 13, 157\u2013163 (1982).","journal-title":"Geom. Dedicata"},{"issue":"2\u20133","key":"911_CR10","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/0012-365X(84)90180-8","volume":"48","author":"LRA Casse","year":"1984","unstructured":"Casse L.R.A., Glynn D.G.: On the uniqueness of $$(q + 1)_{4}$$-arcs of PG(4, q), $$ q= 2^h$$, $$h\\ge 3$$. Discret. Math. 48(2\u20133), 173\u2013186 (1984).","journal-title":"Discret. Math."},{"key":"911_CR11","first-page":"99","volume":"16","author":"A Cossidente","year":"1997","unstructured":"Cossidente A., Hirschfeld J.W.P., Storme L.: Applications of line geometry, III: The quadric Veronesean and the chords of a twisted cubic. Austral. J. Combin. 16, 99\u2013111 (1997).","journal-title":"Austral. J. Combin."},{"issue":"2","key":"911_CR12","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s00373-011-1103-5","volume":"29","author":"AA Davydov","year":"2013","unstructured":"Davydov A.A., Giulietti M., Marcugini S., Pambianco F.: Some combinatorial aspects of constructing bipartite-graph codes. Graphs Combin. 29(2), 187\u2013212 (2013).","journal-title":"Graphs Combin."},{"issue":"1","key":"911_CR13","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10623-015-0070-x","volume":"80","author":"AA Davydov","year":"2016","unstructured":"Davydov A.A., Faina G., Giulietti M., Marcugini S., Pambianco F.: On constructions and parameters of symmetric configurations $$v_k$$. Des. Codes Cryptogr. 80(1), 125\u2013147 (2016).","journal-title":"Des. Codes Cryptogr."},{"key":"911_CR14","unstructured":"Davydov A.A., Marcugini S., Pambianco F.: Twisted cubic and orbits of lines in PG(3,q), arXiv:2103.12655 [math.CO] (2021)."},{"key":"911_CR15","doi-asserted-by":"crossref","unstructured":"Davydov A.A., Marcugini S., Pambianco F.: Twisted cubic and plane-line incidence matrix in PG(3,q), arXiv:2103.11248 [math.CO] (2021).","DOI":"10.1007\/s10623-021-00911-6"},{"key":"911_CR16","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2021.3089129","author":"AA Davydov","year":"2021","unstructured":"Davydov A.A., Marcugini S., Pambianco F.: On cosets weight distributions of the doubly-extended Reed-Solomon codes of codimension 4. IEEE Trans. Inform. Theory (2021). https:\/\/doi.org\/10.1109\/TIT.2021.3089129.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"911_CR17","doi-asserted-by":"publisher","first-page":"3236","DOI":"10.1016\/j.disc.2009.11.040","volume":"310","author":"M Giulietti","year":"2010","unstructured":"Giulietti M., Vincenti R.: Three-level secret sharing schemes from the twisted cubic. Discret. Math. 310, 3236\u20133240 (2010).","journal-title":"Discret. Math."},{"key":"911_CR18","first-page":"353","volume-title":"Handbook of Combinatorial Designs","author":"H Gropp","year":"2006","unstructured":"Gropp H.: Configurations. In: Colbourn C.J., Dinitz J.H. (eds.) Handbook of Combinatorial Designs, 2nd edn, pp. 353\u2013355. Chapman and Hall\/CRC, New York (2006).","edition":"2"},{"key":"911_CR19","doi-asserted-by":"crossref","unstructured":"G\u00fcnay G., Lavrauw M.: On pencils of cubics on the projective line over finite fields of characteristic $$ > 3$$, arXiv:2104.04756 [math.CO][math.AG] (2021).","DOI":"10.1016\/j.ffa.2021.101960"},{"key":"911_CR20","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 University Press, Oxford (1985)."},{"key":"911_CR21","volume-title":"Projective Geometries over Finite Fields","author":"JWP Hirschfeld","year":"1999","unstructured":"Hirschfeld J.W.P.: Projective Geometries over Finite Fields, 2nd edn. Oxford University Press, Oxford (1999).","edition":"2"},{"key":"911_CR22","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/978-1-4613-0283-4_13","volume-title":"Finite Geometries (Proc. 4th Isle of Thorns Conf., July 16-21, 2000), Dev. Math.)","author":"JWP Hirschfeld","year":"2001","unstructured":"Hirschfeld J.W.P., Storme L.: The packing problem in statistics, coding theory and finite projective spaces: Update 2001. In: Blokhuis A., Hirschfeld J.W.P., Jungnickel D., Thas J.A. (eds.) Finite Geometries (Proc. 4th Isle of Thorns Conf., July 16-21, 2000), Dev. Math.), vol. 3, pp. 201\u2013246. Kluwer, Dordrecht (2001)."},{"key":"911_CR23","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.ffa.2014.10.006","volume":"32","author":"JWP Hirschfeld","year":"2015","unstructured":"Hirschfeld J.W.P., Thas J.A.: Open problems in finite projective spaces. Finite Fields Appl. 32, 44\u201381 (2015).","journal-title":"Finite Fields Appl."},{"key":"911_CR24","first-page":"2022","volume-title":"Proc. Int. Symp. Inf. Theory 2006, ISIT 2006","author":"T H\u00f8holdt","year":"2006","unstructured":"H\u00f8holdt T., Justesen J.: Graph codes with Reed-Solomon component codes. Proc. Int. Symp. Inf. Theory 2006, ISIT 2006, pp. 2022\u20132026. IEEE, Seattle (2006)."},{"key":"911_CR25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139172769","volume-title":"Introduction to Finite Fields and their Applications","author":"R Lidl","year":"1994","unstructured":"Lidl R., Niederreiter H.: Introduction to Finite Fields and their Applications, 2nd edn. Cambridge University Press, Cambridge (1994).","edition":"2"},{"key":"911_CR26","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1023\/B:JACO.0000011940.77655.b4","volume":"18","author":"G Lunardon","year":"2003","unstructured":"Lunardon G., Polverino O.: On the Twisted Cubic of PG(3, q). J. Algebr. Combin. 18, 255\u2013262 (2003).","journal-title":"J. Algebr. Combin."},{"key":"911_CR27","first-page":"25","volume-title":"Handbook of Combinatorial Designs","author":"R Mathon","year":"2006","unstructured":"Mathon R., Rosa A.: $$2$$-$$(v, k,\\lambda )$$ Designs of Small Order. In: Colbourn C.J., Dinitz J.H. (eds.) Handbook of Combinatorial Designs, 2nd edn, pp. 25\u201358. Chapman and Hall\/CRC, New York (2006).","edition":"2"},{"key":"911_CR28","first-page":"37","volume":"47","author":"M Zannetti","year":"2010","unstructured":"Zannetti M., Zuanni F.: Note on three-character $$(q + 1)$$-sets in PG(3, q). Austral. J. Combin. 47, 37\u201340 (2010).","journal-title":"Austral. J. Combin."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00911-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-021-00911-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00911-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T23:04:13Z","timestamp":1699398253000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-021-00911-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,27]]},"references-count":28,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["911"],"URL":"https:\/\/doi.org\/10.1007\/s10623-021-00911-6","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,27]]},"assertion":[{"value":"27 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 August 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}