{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T15:38:57Z","timestamp":1772206737109,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T00:00:00Z","timestamp":1665619200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T00:00:00Z","timestamp":1665619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004901","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","doi-asserted-by":"publisher","award":["APQ 01661-17"],"award-info":[{"award-number":["APQ 01661-17"]}],"id":[{"id":"10.13039\/501100004901","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["307037-2019-3"],"award-info":[{"award-number":["307037-2019-3"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s10623-022-01130-3","type":"journal-article","created":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T12:07:43Z","timestamp":1665662863000},"page":"831-851","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve"],"prefix":"10.1007","volume":"91","author":[{"given":"M.","family":"Montanucci","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1026-0546","authenticated-orcid":false,"given":"G.","family":"Tizziotti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,13]]},"reference":[{"key":"1130_CR1","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10623-017-0333-9","volume":"86","author":"D Bartoli","year":"2018","unstructured":"Bartoli D., Montanucci M., Zini G.: Multi point AG codes on the GK maximal curve. Des. Codes Cryptogr. 86, 161\u2013177 (2018).","journal-title":"Des. Codes Cryptogr."},{"key":"1130_CR2","doi-asserted-by":"publisher","first-page":"2315","DOI":"10.1007\/s10623-017-0450-5","volume":"86","author":"D Bartoli","year":"2018","unstructured":"Bartoli D., Montanucci M., Zini G.: AG codes and AG quantum codes from the GGS curve. Des. Codes Cryptogr. 86, 2315\u20132344 (2018).","journal-title":"Des. Codes Cryptogr."},{"key":"1130_CR3","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.jpaa.2005.09.017","volume":"207","author":"P Beelen","year":"2006","unstructured":"Beelen P., Tutas N.: A generalization of the Weierstrass semigroup. J. Pure Appl. Algebra 207, 243\u2013260 (2006).","journal-title":"J. Pure Appl. Algebra"},{"key":"1130_CR4","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1112\/jlms.12144","volume":"98","author":"P Beelen","year":"2018","unstructured":"Beelen P., Montanucci M.: A new family of maximal curves. J. Lond. Math. Soc. 98, 573\u2013592 (2018).","journal-title":"J. Lond. Math. Soc."},{"key":"1130_CR5","doi-asserted-by":"publisher","first-page":"1595","DOI":"10.1007\/s10623-020-00757-4","volume":"88","author":"M Br\u00e1s-Amor\u00f3s","year":"2020","unstructured":"Br\u00e1s-Amor\u00f3s M., Castellanos A.S.: Weierstrass semigroup at $$m+1$$ rational points in maximal curves which cannot be covered by the Hermitian curve. Des. Codes Cryptogr. 88, 1595\u20131616 (2020).","journal-title":"Des. Codes Cryptogr."},{"key":"1130_CR6","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10711-008-9337-y","volume":"139","author":"C Carvalho","year":"2009","unstructured":"Carvalho C., Kato T.: On Weierstrass semigroup and sets: a review with new results. Geom. Dedicata. 139, 139\u2013195 (2009).","journal-title":"Geom. Dedicata."},{"key":"1130_CR7","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/s10623-005-6403-4","volume":"35","author":"C Carvalho","year":"2005","unstructured":"Carvalho C., Torres F.: On Goppa codes and Weierstrass gaps at several points. Des. Codes Cryptogr. 35, 211\u2013225 (2005).","journal-title":"Des. Codes Cryptogr."},{"key":"1130_CR8","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1109\/TIT.2015.2511787","volume":"62","author":"AS Castellanos","year":"2016","unstructured":"Castellanos A.S., Tizziotti G.: Two-point AG codes on the GK maximal curves. IEEE Trans. Inf. Theory 62, 681\u2013686 (2016).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"1130_CR9","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1090\/S0002-9939-1990-0990420-2","volume":"108","author":"F Delgado","year":"1990","unstructured":"Delgado F.: The symmetry of the Weierstrass generalized semigroups and affine embeddings. Proc. Am. Math. Soc. 108(3), 627\u2013631 (1990).","journal-title":"Proc. Am. Math. Soc."},{"key":"1130_CR10","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s00574-012-0022-2","volume":"43","author":"I Duursma","year":"2012","unstructured":"Duursma I., Mak K.H.: On maximal curves which are not Galois subcovers of the Hermitian curve. Bull. Braz. Math. Soc. 43, 453\u2013465 (2012).","journal-title":"Bull. Braz. Math. Soc."},{"key":"1130_CR11","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1016\/j.ffa.2012.06.005","volume":"18","author":"IM Duursma","year":"2012","unstructured":"Duursma I.M., Park S.: Delta sets for divisors supported in two points. Finite Fields Appl. 18, 865\u2013885 (2012).","journal-title":"Finite Fields Appl."},{"key":"1130_CR12","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1109\/TIT.2009.2034826","volume":"56","author":"S Fanali","year":"2010","unstructured":"Fanali S., Giulietti M.: One-point AG codes on the GK maximal curves. IEEE Trans. Inf. Theory 56, 202\u2013210 (2010).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1130_CR13","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1515\/advgeom.2011.046","volume":"12","author":"S Fanali","year":"2012","unstructured":"Fanali S., Giulietti M.: Quotient curves of the GK curve. Adv. Geom. 12, 239\u2013268 (2012).","journal-title":"Adv. Geom."},{"key":"1130_CR14","volume-title":"Algebraic Curves: An Introduction to Algebraic Geometry","author":"W Fulton","year":"1969","unstructured":"Fulton W.: Algebraic Curves: An Introduction to Algebraic Geometry. Addison Wesley, Boston (1969)."},{"key":"1130_CR15","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1515\/advgeom.2010.020","volume":"10","author":"A Garcia","year":"2010","unstructured":"Garcia A., G\u00fcneri C., Stichtenoth H.: A generalization of the Giulietti-Korchm\u00e1ros maximal curve. Adv. Geom. 10, 427\u2013434 (2010).","journal-title":"Adv. Geom."},{"key":"1130_CR16","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0022-4049(93)90039-V","volume":"84","author":"A Garcia","year":"1993","unstructured":"Garcia A., Kim S.J., Lax R.F.: Consecutive Weierstrass gaps and minimum distance of Goppa codes. J. Pure Appl. Algebra 84, 199\u2013207 (1993).","journal-title":"J. Pure Appl. Algebra"},{"key":"1130_CR17","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s00208-008-0270-z","volume":"343","author":"M Giulietti","year":"2009","unstructured":"Giulietti M., Korchm\u00e1ros G.: A new family of maximal curves over a finite field. Math. Ann. 343, 229\u2013245 (2009).","journal-title":"Math. Ann."},{"key":"1130_CR18","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.ffa.2016.05.005","volume":"41","author":"M Giulietti","year":"2016","unstructured":"Giulietti M., Montanucci M., Zini G.: On maximal curves that are not quotients of the Hermitian curve. Finite Fields Appl. 41, 72\u201388 (2016).","journal-title":"Finite Fields Appl."},{"key":"1130_CR19","doi-asserted-by":"publisher","first-page":"279","DOI":"10.3934\/amc.2020020","volume":"14","author":"C Hu","year":"2020","unstructured":"Hu C., Yang S.: Multi-point Codes from the GGS Curves. Adv. Math. Commun. 14, 279\u2013299 (2020).","journal-title":"Adv. Math. Commun."},{"key":"1130_CR20","doi-asserted-by":"publisher","first-page":"1720","DOI":"10.1109\/18.476245","volume":"41","author":"C Kirfel","year":"1995","unstructured":"Kirfel C., Pellikaan R.: The minimum distance of codes in an array coming from telescopic semigroups. IEEE Trans. Inf. Theory 41, 1720\u20131732 (1995).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1130_CR21","first-page":"729","volume":"305","author":"G Lachaud","year":"1987","unstructured":"Lachaud G.: Sommes d\u2019 Eisenstein et nombre de points de certaines courbes alg\u00e9briques sur les corps finis. C.R. Acad. Sci. Paris 305, 729\u2013732 (1987).","journal-title":"C.R. Acad. Sci. Paris"},{"key":"1130_CR22","unstructured":"Landi L., Vicino L.: Two-point AG codes from the Beelen-Montanucci maximal curve, preprint, arXiv:2106.14564."},{"key":"1130_CR23","doi-asserted-by":"crossref","unstructured":"Matthews G.L.: The Weierstrass semigroup of an $$m$$-tuple of collinear points on a Hermitian curve, Lecture note in Comput. Sci., , vol. 2948, pp. 12\u201324. Springer, Berlin (2004).","DOI":"10.1007\/978-3-540-24633-6_2"},{"key":"1130_CR24","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s10623-004-4038-5","volume":"37","author":"GL Matthews","year":"2005","unstructured":"Matthews G.L.: Weierstrass semigroups and codes from a quotient of the Hermitian curve. Des. Codes Cryptogr. 37, 473\u2013492 (2005).","journal-title":"Des. Codes Cryptogr."},{"key":"1130_CR25","doi-asserted-by":"publisher","first-page":"111810","DOI":"10.1016\/j.disc.2020.111810","volume":"343","author":"M Montanucci","year":"2020","unstructured":"Montanucci M., Pallozzi Lavorante V.: AG codes from the second generalization of the GK maximal curve. Discret. Math. 343, 111810 (2020).","journal-title":"Discret. Math."},{"key":"1130_CR26","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.ffa.2019.03.005","volume":"58","author":"JJ Moyano-Fern\u00e1ndez","year":"2019","unstructured":"Moyano-Fern\u00e1ndez J.J., Ten\u00f3rio W., Torres F.: Generalized Weierstrass semigroups and their Poincar\u00e9 series. Finite Fields Appl. 58, 46\u201369 (2019).","journal-title":"Finite Fields Appl."},{"key":"1130_CR27","volume-title":"Algebraic Function Fields and Codes","author":"H Stichtenoth","year":"1993","unstructured":"Stichtenoth H.: Algebraic Function Fields and Codes. Springer, Berlin (1993)."},{"key":"1130_CR28","doi-asserted-by":"publisher","first-page":"1122","DOI":"10.1016\/j.jpaa.2015.08.010","volume":"220","author":"S Tafazolian","year":"2016","unstructured":"Tafazolian S., Teher\u00e1n-Herrera A., Torres F.: Further examples of maximal curves which cannot be covered by the Hermitian curve. J. Pure Appl. Algebra 220, 1122\u20131132 (2016).","journal-title":"J. Pure Appl. Algebra"},{"key":"1130_CR29","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.ffa.2019.02.007","volume":"57","author":"W Ten\u00f3rio","year":"2019","unstructured":"Ten\u00f3rio W., Tizziotti G.: Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables. Finite Fields Appl. 57, 230\u2013248 (2019).","journal-title":"Finite Fields Appl."},{"key":"1130_CR30","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/s00574-018-0116-6","volume":"50","author":"W Ten\u00f3rio","year":"2019","unstructured":"Ten\u00f3rio W., Tizziotti G.: On Weierstrass gaps at several points. Bull. Braz. Math. Soc. 50, 543\u2013559 (2019).","journal-title":"Bull. Braz. Math. Soc."},{"key":"1130_CR31","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s00574-017-0059-3","volume":"49","author":"G Tizziotti","year":"2018","unstructured":"Tizziotti G., Castellanos A.S.: Weierstrass semigroup and pure gaps at several points on the GK curve. Bull. Braz. Math. Soc. 49, 419\u2013429 (2018).","journal-title":"Bull. Braz. Math. Soc."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01130-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-022-01130-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01130-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T18:19:55Z","timestamp":1678472395000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-022-01130-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,13]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["1130"],"URL":"https:\/\/doi.org\/10.1007\/s10623-022-01130-3","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,13]]},"assertion":[{"value":"15 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 October 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}