{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:59:30Z","timestamp":1772283570291,"version":"3.50.1"},"reference-count":30,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2000,3,1]],"date-time":"2000-03-01T00:00:00Z","timestamp":951868800000},"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":4886,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theoretical Computer Science"],"published-print":{"date-parts":[[2000,3]]},"DOI":"10.1016\/s0304-3975(99)00200-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T01:51:05Z","timestamp":1027648265000},"page":"283-308","source":"Crossref","is-referenced-by-count":7,"title":["On covering radii and coset weight distributions of extremal binary self-dual codes of length 40"],"prefix":"10.1016","volume":"235","author":[{"given":"Michio","family":"Ozeki","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0304-3975(99)00200-5_BIB1","doi-asserted-by":"crossref","unstructured":"E.F.Assmus, Jr., H.F. Mattson, Jr., New 5-designs, J. Combin. Theory Ser. A 6 (1969) 122\u2013151.","DOI":"10.1016\/S0021-9800(69)80115-8"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB2","doi-asserted-by":"crossref","unstructured":"E.F. Assmus, Jr., V. Pless, On the covering radius of extremal self-dual codes, IEEE Trans. Inform. Theory IT-29 (1983) 359\u2013363.","DOI":"10.1109\/TIT.1983.1056681"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB3","doi-asserted-by":"crossref","first-page":"12","DOI":"10.3792\/pjaa.72.12","article-title":"Construction of Jacobi forms from certain combinatorial polynomials","volume":"72","author":"Bannai","year":"1996","journal-title":"Proc. Japan Acad. Ser. A"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB4","unstructured":"E. Bannai, E. Bannai, M. Ozeki, S. Teranishi, Rings of simultaneous invariants for the MacWilliams\u2013Gleason group, in preparation."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB5","unstructured":"G. Batut, D. Bernardi, H. Cohen, M. Olivier, PARI-GP (a computer algebra system)."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB6","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/18.86979","article-title":"Weight enumerators of self-dual codes","volume":"37","author":"Brualdi","year":"1991","journal-title":"IEEE Trans. Inform. Theory"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB7","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/0012-365X(90)90208-Y","article-title":"Extremal doubly-even codes of length 40 derived from Hadamard matrices of order 20","volume":"82","author":"Bussemaker","year":"1990","journal-title":"Discrete Math."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB8","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0097-3165(92)90003-D","article-title":"The binary self-dual codes of length up to 32: a revised enumeration","volume":"60","author":"Conway","year":"1992","journal-title":"J. Combin. Theory Ser. A"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB9","series-title":"Sphere Packings, Lattices and Groups","author":"Conway","year":"1988"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB10","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/S0019-9958(73)80007-5","article-title":"Four fundamental parameters of a code and their combinatorial significance","volume":"23","author":"Delsarte","year":"1973","journal-title":"Inform. and Control"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB11","unstructured":"P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Re. Rep. Suppl. 10 (1973)."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB12","unstructured":"A.M. Gleason, Weight polynomials of self-dual codes and the MacWilliams identities, in: Actes Congres Int. de Mathematique 1970, 3 Gauthier-Villars, Paris, 1971, pp. 211\u2013215."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB13","first-page":"260","article-title":"Binary self-dual codes with automorphisms of odd order","volume":"19","author":"Iorgov","year":"1983","journal-title":"Problems Inform. Transmission"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB14","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1007\/BF01097979","article-title":"Cosets of an extremal binary code of dimension 48","volume":"63","author":"Ivanov","year":"1993","journal-title":"J. Sov. Math."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB15","doi-asserted-by":"crossref","unstructured":"F. Klein, Vorlesungen \u00fcber das Ikosaeder, Birkh\u00e4user, B.G.Teubner, Basel, 1993.","DOI":"10.1007\/978-3-0348-8594-2"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB16","unstructured":"F.J. MacWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB17","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/0097-3165(87)90034-3","article-title":"Hadamard matrices and doubly even error correcting codes","volume":"44","author":"Ozeki","year":"1987","journal-title":"J. Combin. Theory Ser. A"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB18","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0022-314X(88)90059-5","article-title":"Examples of even unimodular extremal lattices of rank 40 and their Siegel theta series of degree 2","volume":"28","author":"Ozeki","year":"1988","journal-title":"J. Numer. Theory"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB19","unstructured":"M. Ozeki, On the relation between the invariants of a doubly even self-dual binary code C and the invariants of the even unimodular lattices L(C) defined from the code C, in: Meeting on Algebraic Combinatorics, Suuri Kaiseki Kenkyuusho Koukyuuroku No. 671, Research Institute of Mathematical Sciences in Kyouto Univ, 1988."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB20","unstructured":"M. Ozeki, Determination of the ring of simultaneous invariants for a group associated with MacWilliams identity (an intermediate report of a joint work with E. Bannai), in: Meeting on algebraic combinatorics, Suuri Kaiseki Kenkyuusho Koukyuuroku No. ??? Research Institute of Mathematical Sciences in Kyouto Univ, 1995, unpublished."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB21","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1017\/S0305004196001399","article-title":"On the notion of Jacobi polynomials for codes","volume":"121","author":"Ozeki","year":"1997","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB22","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/0012-365X(72)90034-9","article-title":"A classification of Self-Orthogonal Codes over GF(2)","volume":"3","author":"Pless","year":"1972","journal-title":"Discrete Math."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB23","series-title":"An Introduction to the Theory of Error-Correcting Codes","author":"Pless","year":"1982"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB24","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0097-3165(75)90042-4","article-title":"On the classification and enumeration of self-dual codes","volume":"18","author":"Pless","year":"1975","journal-title":"J. Combin. Theory Ser. A"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB25","series-title":"Vorlesungen \u00fcber Invariantentheorie","author":"Schur","year":"1968"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB26","doi-asserted-by":"crossref","first-page":"364","DOI":"10.4153\/CJM-1953-042-7","article-title":"Finite unitary reflection groups","volume":"5","author":"Shephard","year":"1953","journal-title":"Canad. J. Math."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB27","doi-asserted-by":"crossref","first-page":"82","DOI":"10.2307\/2319929","article-title":"Error-correcting codes and invariant theory: new applications of a nineteenth-century technique","volume":"84","author":"Sloane","year":"1977","journal-title":"Amer. Math. Mon."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB28","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1090\/pspum\/034\/525331","article-title":"Self-dual codes and lattices, in Relations between Combinatorics and Other Parts of Mathematics","volume":"34","author":"Sloane","year":"1979","journal-title":"Proc. Symp. in Pure Math."},{"key":"10.1016\/S0304-3975(99)00200-5_BIB29","first-page":"270","article-title":"Hadamard-type block designs and self-dual codes","volume":"19","author":"Tonchev","year":"1983","journal-title":"Problems Inform. Transmission"},{"key":"10.1016\/S0304-3975(99)00200-5_BIB30","doi-asserted-by":"crossref","first-page":"3459","DOI":"10.1007\/BF01100113","article-title":"Combinatorial properties of extremal doubly-even codes of length 48","volume":"57","author":"Venkov","year":"1991","journal-title":"J. Sov. Math."}],"container-title":["Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397599002005?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397599002005?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T08:53:59Z","timestamp":1555318439000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0304397599002005"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,3]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,3]]}},"alternative-id":["S0304397599002005"],"URL":"https:\/\/doi.org\/10.1016\/s0304-3975(99)00200-5","relation":{},"ISSN":["0304-3975"],"issn-type":[{"value":"0304-3975","type":"print"}],"subject":[],"published":{"date-parts":[[2000,3]]}}}