{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T18:29:35Z","timestamp":1687804175930},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2019,1,5]],"date-time":"2019-01-05T00:00:00Z","timestamp":1546646400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["209918"],"id":[{"id":"10.13039\/501100003141","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":[[2019,9]]},"DOI":"10.1007\/s10623-018-00603-8","type":"journal-article","created":{"date-parts":[[2019,1,5]],"date-time":"2019-01-05T05:23:28Z","timestamp":1546665808000},"page":"2027-2042","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Projective Reed\u2013Muller type codes on higher dimensional scrolls"],"prefix":"10.1007","volume":"87","author":[{"given":"C\u00edcero","family":"Carvalho","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8349-0364","authenticated-orcid":false,"given":"Xavier","family":"Ram\u00edrez-Mondrag\u00f3n","sequence":"additional","affiliation":[]},{"given":"Victor G. L.","family":"Neumann","sequence":"additional","affiliation":[]},{"given":"Horacio","family":"Tapia-Recillas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,5]]},"reference":[{"key":"603_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0913-3","volume-title":"Gr\u00f6bner Bases","author":"T Becker","year":"1993","unstructured":"Becker T., Weispfenning W.: Gr\u00f6bner Bases. Springer, New York (1993)."},{"key":"603_CR2","unstructured":"Beelen, P., Datta, M., Ghorpade, S.R.: A combinatorial approach to the number of solutions of systems of homogeneous polynomial equations over finite fields. \n arXiv:1807.01683v2\n \n (2018)"},{"issue":"4","key":"603_CR3","doi-asserted-by":"publisher","first-page":"1451","DOI":"10.1090\/proc\/13863","volume":"146","author":"P Beelen","year":"2018","unstructured":"Beelen P., Datta M., Ghorpade S.R.: Maximum number of common zeros of homogeneous polynomials over finite fields. Proc. Am. Math. Soc. 146(4), 1451\u20131468 (2018).","journal-title":"Proc. Am. Math. Soc."},{"key":"603_CR4","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. Symb. Comput. 24, 235\u2013265 (1997).","journal-title":"J. Symb. Comput."},{"key":"603_CR5","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.ffa.2015.09.004","volume":"37","author":"C Carvalho","year":"2016","unstructured":"Carvalho C., Neumann V.G.L.: Projective Reed-Muller type codes on rational normal scrolls. Finite Fields Appl. 37, 85\u2013107 (2016).","journal-title":"Finite Fields Appl."},{"key":"603_CR6","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s00574-016-0010-z","volume":"48","author":"C Carvalho","year":"2017","unstructured":"Carvalho C., Neumann V.G.L., Lopez H.: Projective nested cartesian codes. Bull. Braz. Math. Soc. 48, 283\u2013302 (2017).","journal-title":"Bull. Braz. Math. Soc."},{"key":"603_CR7","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s10623-012-9692-4","volume":"66","author":"A Couvreur","year":"2013","unstructured":"Couvreur A., Duursma I.: Evaluation codes from smooth quadric surfaces and twisted Segre varieties. Des. Codes Cryptogr. 66, 291\u2013303 (2013).","journal-title":"Des. Codes Cryptogr."},{"key":"603_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-35651-8","volume-title":"Ideals, Varieties, and Algorithms","author":"D Cox","year":"2007","unstructured":"Cox D., Little J., O\u2019Shea D.: Ideals, Varieties, and Algorithms, 3rd edn. Springer, New York (2007).","edition":"3"},{"key":"603_CR9","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s002000000047","volume":"11","author":"I Duursma","year":"2001","unstructured":"Duursma I., Renter\u00eda C., Tapia-Recillas H.: Reed Muller codes on complete intersections. Appl. Algebra Eng. Commun. Comput. (AAECC) 11, 455\u2013462 (2001).","journal-title":"Appl. Algebra Eng. Commun. Comput. (AAECC)"},{"key":"603_CR10","doi-asserted-by":"publisher","unstructured":"Gonz\u00e1lez-Sarabia, M., Mart\u00ednez-Bernal, J., Villarreal, R.H., V\u00edvares, C.E.: Generalized minimum distance functions. J. Algebr. Comb. \n https:\/\/doi.org\/10.1007\/s10801-018-0855-x\n \n (2018)","DOI":"10.1007\/s10801-018-0855-x"},{"key":"603_CR11","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/S1071-5797(02)90360-6","volume":"8","author":"M Gonz\u00e1lez-Sarabia","year":"2002","unstructured":"Gonz\u00e1lez-Sarabia M., Renter\u00eda C., Tapia Recillas H.: Reed-Muller type codes over the segre variety. Finite Fields Appl. 8, 511\u2013518 (2002).","journal-title":"Finite Fields Appl."},{"key":"603_CR12","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s00200-003-0136-2","volume":"14","author":"M Gonz\u00e1lez-Sarabia","year":"2004","unstructured":"Gonz\u00e1lez-Sarabia M., Renter\u00eda C.: The dual code of some Reed-Muller-type codes. Appl. Algebra Eng. Commun. Comput. (AAECC) 14, 329\u2013333 (2004).","journal-title":"Appl. Algebra Eng. Commun. Comput. (AAECC)"},{"key":"603_CR13","unstructured":"Harris, J.: Algebraic Geometry: A First Course, 3rd. edn, Springer, GTM, no. 133 (1995)"},{"key":"603_CR14","volume-title":"Coding Theory and Applications. Lecture Notes in Computer Science","author":"G Lachaud","year":"1988","unstructured":"Lachaud G.: Projective Reed-Muller codes. In: Cohen G., Godlewski P. (eds.) Coding Theory and Applications. Lecture Notes in Computer Science, vol. 311. Springer, Berlin (1988)."},{"issue":"2","key":"603_CR15","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1080\/00927879708825862","volume":"25","author":"C Renter\u00eda","year":"1997","unstructured":"Renter\u00eda C., Tapia-Recillas H.: Reed-Muller codes: an ideal theory approach. Commun. Algebra 25(2), 401\u2013413 (1997).","journal-title":"Commun. Algebra"},{"key":"603_CR16","doi-asserted-by":"crossref","unstructured":"Renter\u00eda, C., Tapia-Recillas, H.: Reed-Muller type codes on the Veronese Variety over finite fields. In: Buchmann, J., Hoholdt, T., Stichtenoth, H., Tapia-Recillas, H. (eds.) Coding Theory, Cryptography and Related Areas, ISBN 3-540-66248-0, pp. 237\u2013243 , Springer, New York (2000)","DOI":"10.1007\/978-3-642-57189-3_21"},{"issue":"6","key":"603_CR17","doi-asserted-by":"publisher","first-page":"1567","DOI":"10.1109\/18.104317","volume":"37","author":"AB S\u00f6rensen","year":"1991","unstructured":"S\u00f6rensen A.B.: Projective Reed-Muller codes. IEEE Trans. Inform. Theory 37(6), 1567\u20131576 (1991).","journal-title":"IEEE Trans. Inform. Theory"},{"key":"603_CR18","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.ffa.2016.01.006","volume":"39","author":"A Tochimani","year":"2016","unstructured":"Tochimani A., Pinto M.V., Villarreal R.H.: Direct products in projective Segre codes. Finite Fields Appl. 39, 96\u2013110 (2016).","journal-title":"Finite Fields Appl."},{"key":"603_CR19","volume-title":"Applied Combinatorics","author":"A Tucker","year":"2012","unstructured":"Tucker A.: Applied Combinatorics, 6th edn. Wiley, New York (2012).","edition":"6"},{"key":"603_CR20","doi-asserted-by":"crossref","unstructured":"van Lint, J.H.: Coding Theory, Lect. Notes Math., 2nd edn, vol. 201. Springer, Berlin (1973)","DOI":"10.1007\/978-3-540-36657-7"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-018-00603-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-018-00603-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-018-00603-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,5]],"date-time":"2020-01-05T00:13:52Z","timestamp":1578183232000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-018-00603-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,5]]},"references-count":20,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["603"],"URL":"https:\/\/doi.org\/10.1007\/s10623-018-00603-8","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,5]]},"assertion":[{"value":"2 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}