{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T05:17:15Z","timestamp":1712380635451},"reference-count":17,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[1999,7,1]],"date-time":"1999-07-01T00:00:00Z","timestamp":930787200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":5130,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[1999,7]]},"DOI":"10.1016\/s0012-365x(99)00032-1","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T17:35:45Z","timestamp":1027618545000},"page":"1-21","source":"Crossref","is-referenced-by-count":5,"title":["Niemeier lattices and Type II codes over Z4"],"prefix":"10.1016","volume":"205","author":[{"given":"Alexis","family":"Bonnecaze","sequence":"first","affiliation":[]},{"given":"Philippe","family":"Gaborit","sequence":"additional","affiliation":[]},{"given":"Masaaki","family":"Harada","sequence":"additional","affiliation":[]},{"given":"Masaaki","family":"Kitazume","sequence":"additional","affiliation":[]},{"given":"Patrick","family":"Sol\u00e9","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0012-365X(99)00032-1_BIB1","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1109\/18.370138","article-title":"Quaternary quadratic residue codes and unimodular lattices","volume":"41","author":"Bonnecaze","year":"1995","journal-title":"IEEE Trans. Inform. Theory"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB2","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1109\/18.568705","article-title":"Type II codes over Z4","volume":"43","author":"Bonnecaze","year":"1997","journal-title":"IEEE Trans. Inform. Theory"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB4","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1023\/A:1008639004036","article-title":"Double circulant codes over Z4 and even unimodular lattices","volume":"6","author":"Calderbank","year":"1997","journal-title":"J. Algebraic Combin."},{"key":"10.1016\/S0012-365X(99)00032-1_BIB5","doi-asserted-by":"crossref","unstructured":"H. Cohen, A Course in Computational Algebraic Number Theory, Springer, New York, 1993.","DOI":"10.1007\/978-3-662-02945-9"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB6","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1112\/S0025579300009244","article-title":"Extremal self-dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24","volume":"25","author":"Conway","year":"1978","journal-title":"Mathematika"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB7","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0097-3165(93)90070-O","article-title":"Self-dual codes over the integers modulo 4","volume":"62","author":"Conway","year":"1993","journal-title":"J. Combin. Theory Ser. A"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB8","doi-asserted-by":"crossref","unstructured":"J.H. Conway, N.J.A. Sloane, Sphere Packing, Lattices and Groups, 2nd ed., Springer, New York, 1993.","DOI":"10.1007\/978-1-4757-2249-9"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB9","doi-asserted-by":"crossref","unstructured":"C. Dong, H. Li, G. Mason, S.P. Norton, Associative subalgebras of the Griess algebra and related topics, in: The Monster and Lie Algebras, Ohio State Univ. Math. Res. Inst. Publ., 7, de Gruyter, Berlin, 1998, 27\u201342.","DOI":"10.1515\/9783110801897.27"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB10","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1109\/18.651058","article-title":"All self-dual Z4 codes of length 15 or less are known","volume":"44","author":"Fields","year":"1998","journal-title":"IEEE Trans. Inform. Theory"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB11","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1008254008212","article-title":"New extremal Type II codes over Z4","volume":"13","author":"Harada","year":"1998","journal-title":"Des. Codes Cryptogr."},{"key":"10.1016\/S0012-365X(99)00032-1_BIB12","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF01198572","article-title":"Selbstduale Codes \u00fcber dem Ring der ganzen Zahlen modulo 4","volume":"53","author":"Klemm","year":"1989","journal-title":"Archiv. Math."},{"key":"10.1016\/S0012-365X(99)00032-1_BIB13","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0012-365X(93)E0088-L","article-title":"A new construction of lattices from codes over GF(3)","volume":"135","author":"Montague","year":"1994","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(99)00032-1_BIB14","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/0022-314X(73)90068-1","article-title":"Definete quadratische Formen der Dimension 24 und Diskriminante 1","volume":"5","author":"Niemeier","year":"1973","journal-title":"J. Number Theory"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB15","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1006\/ffta.1996.0172","article-title":"Cyclic self-dual Z4-codes","volume":"3","author":"Pless","year":"1997","journal-title":"Finite Fields Appl."},{"key":"10.1016\/S0012-365X(99)00032-1_BIB16","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0012-365X(87)90213-5","article-title":"A group algebra construction of binary even self dual codes","volume":"65","author":"Wolfmann","year":"1987","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(99)00032-1_BIB17","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1109\/TIT.1983.1056726","article-title":"A permutation decoding of the (24,12,8) Golay code","volume":"29","author":"Wolfmann","year":"1983","journal-title":"IEEE Trans. Inform. Theory"},{"key":"10.1016\/S0012-365X(99)00032-1_BIB18","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/BF02940750","article-title":"Eine Identit\u00e4t zwischen Modulformen zweiten Grades","volume":"14","author":"Witt","year":"1941","journal-title":"Abhand. Math. Semin. der Univ. Hamburg"}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X99000321?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X99000321?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T18:25:31Z","timestamp":1556130331000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0012365X99000321"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,7]]},"references-count":17,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1999,7]]}},"alternative-id":["S0012365X99000321"],"URL":"https:\/\/doi.org\/10.1016\/s0012-365x(99)00032-1","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[1999,7]]}}}