{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T23:09:08Z","timestamp":1771974548361,"version":"3.50.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s10623-018-0567-1","type":"journal-article","created":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T07:17:11Z","timestamp":1541056631000},"page":"817-830","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The weight spectrum of certain affine Grassmann codes"],"prefix":"10.1007","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9714-7249","authenticated-orcid":false,"given":"Fernando","family":"Pi\u00f1ero","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prasant","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,11,1]]},"reference":[{"key":"567_CR1","doi-asserted-by":"publisher","first-page":"3166","DOI":"10.1109\/TIT.2010.2048470","volume":"56","author":"P Beelen","year":"2010","unstructured":"Beelen P., Ghorpade S.R., H\u00f8holdt T.: Affine Grassmann codes. IEEE Trans. Inf. Theory 56, 3166\u20133176 (2010).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"567_CR2","doi-asserted-by":"publisher","first-page":"3843","DOI":"10.1109\/TIT.2012.2187171","volume":"58","author":"P Beelen","year":"2012","unstructured":"Beelen P., Ghorpade S.R., H\u00f8holdt T.: Duals of affine Grassmann codes and their relatives. IEEE Trans. Inf. Theory 58, 3843\u20133855 (2012).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"567_CR3","doi-asserted-by":"publisher","first-page":"1535","DOI":"10.1109\/18.850689","volume":"46","author":"H Chen","year":"2000","unstructured":"Chen H.: On the minimum distance of Schubert codes. IEEE Trans. Inf. Theory 46, 1535\u20131538 (2000).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"567_CR4","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1007\/978-3-642-57189-3_11","volume-title":"Coding Theory, Cryptography and Related Areas (Guanajuato, 1998)","author":"SR Ghorpade","year":"2000","unstructured":"Ghorpade S.R., Lachaud G.: Higher weights of Grassmann codes. In: Buchmann J., Hoeholdt T., Stichtenoth H., Tapia-Recillas H. (eds.) Coding Theory, Cryptography and Related Areas (Guanajuato, 1998), pp. 122\u2013131. Springer, Berlin (2000)."},{"key":"567_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ffa.2017.08.014","volume":"49","author":"SR Ghorpade","year":"2018","unstructured":"Ghorpade S.R., Singh P.: Minimum distance and the minimum weight codewords of Schubert codes. Finite Fields Appl. 49, 1\u201328 (2018).","journal-title":"Finite Fields Appl."},{"key":"567_CR6","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1016\/j.ffa.2004.09.002","volume":"11","author":"SR Ghorpade","year":"2005","unstructured":"Ghorpade S.R., Tsfasman M.A.: Schubert varieties, linear codes and enumerative combinatorics. Finite Fields Appl. 11, 684\u2013699 (2005).","journal-title":"Finite Fields Appl."},{"key":"567_CR7","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1023\/B:DESI.0000035470.05639.2b","volume":"33","author":"L Guerra","year":"2004","unstructured":"Guerra L., Vincenti R.: On the linear codes arising from Schubert varieties. Des. Codes Cryptogr. 33, 173\u2013180 (2004).","journal-title":"Des. Codes Cryptogr."},{"key":"567_CR8","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1109\/TIT.2012.2219497","volume":"59","author":"K Kaipa","year":"2013","unstructured":"Kaipa K., Pillai H.: Weight spectrum of codes associated with the Grassmannian \n                    \n                      \n                    \n                    $$G(3,7)$$\n                    \n                      \n                        \n                          G\n                          (\n                          3\n                          ,\n                          7\n                          )\n                        \n                      \n                    \n                  . IEEE Trans. Inf. Theory 59, 983\u2013993 (2013).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"567_CR9","volume-title":"Algebra. Graduate Texts in Mathematics","author":"S Lang","year":"2002","unstructured":"Lang S.: Algebra. Graduate Texts in Mathematics, vol. 211. Springer, New York (2002)."},{"key":"567_CR10","unstructured":"Nogin D.Yu.: Codes associated to Grassmannians. In: Pellikaan R., Perret M., Vl\u0103du\u0163 S.G. (eds.) Arithmetic, Geometry and Coding Theory (Luminy, 1993), pp. 145\u2013154. Walter de Gruyter, Berlin (1996)."},{"key":"567_CR11","unstructured":"Nogin D.Yu.: The spectrum of codes associated with the Grassmannian variety \n                    \n                      \n                    \n                    $$G(3,6)$$\n                    \n                      \n                        \n                          G\n                          (\n                          3\n                          ,\n                          6\n                          )\n                        \n                      \n                    \n                  . Probl. Inf. Transm. 33, 114\u2013123 (1997)."},{"key":"567_CR12","doi-asserted-by":"publisher","first-page":"1425","DOI":"10.1109\/TIT.2017.2650207","volume":"63","author":"F Pi\u00f1ero","year":"2017","unstructured":"Pi\u00f1ero F.: The structure of dual Schubert Union Codes. IEEE Trans. Inf. Theory 63, 1425\u20131433 (2017).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"567_CR13","doi-asserted-by":"publisher","unstructured":"Pi\u00f1ero F., Singh P.: A note on the weight distribution of Schubert codes. Des. Codes Cryptogr. (2018). \n                    https:\/\/doi.org\/10.1007\/s10623-018-0477-2\n                    \n                  .","DOI":"10.1007\/s10623-018-0477-2"},{"key":"567_CR14","first-page":"257","volume":"57","author":"CT Ryan","year":"1987","unstructured":"Ryan C.T.: An application of Grassmann varieties to coding theory. Congr. Numer. 57, 257\u2013271 (1987).","journal-title":"Congr. Numer."},{"key":"567_CR15","first-page":"273","volume":"57","author":"CT Ryan","year":"1987","unstructured":"Ryan C.T.: Projective codes based on Grassmann varieties. Congr. Numer. 57, 273\u2013279 (1987).","journal-title":"Congr. Numer."},{"key":"567_CR16","unstructured":"SageMath.: The Sage Mathematics Software System (Version 7.2.3). The Sage Developers. \n                    http:\/\/www.sagemath.org\n                    \n                   (2017)."},{"key":"567_CR17","series-title":"Math. Surv. Monogr.","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/139","volume-title":"Algebraic Geometric Codes: Basic Notions","author":"M Tsfasman","year":"2007","unstructured":"Tsfasman M., Vl\u0103du\u0163 S., Nogin D.: Algebraic Geometric Codes: Basic Notions, vol. 139. Math. Surv. Monogr.Amer. Math. Soc., Providence, RI (2007)."},{"key":"567_CR18","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1109\/TIT.2007.911283","volume":"54","author":"X Xiang","year":"2008","unstructured":"Xiang X.: On the minimum distance conjecture for Schubert codes. IEEE Trans. Inf. Theory 54, 486\u2013488 (2008).","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-018-0567-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-018-0567-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-018-0567-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,11,1]],"date-time":"2019-11-01T07:45:59Z","timestamp":1572594359000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-018-0567-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,1]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["567"],"URL":"https:\/\/doi.org\/10.1007\/s10623-018-0567-1","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,1]]},"assertion":[{"value":"1 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}