{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T10:06:37Z","timestamp":1762250797377,"version":"3.41.2"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1999,12,1]],"date-time":"1999-12-01T00:00:00Z","timestamp":944006400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1999,12,1]],"date-time":"1999-12-01T00:00:00Z","timestamp":944006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Designs, Codes and Cryptography"],"published-print":{"date-parts":[[1999,12]]},"DOI":"10.1023\/a:1008368615935","type":"journal-article","created":{"date-parts":[[2002,12,22]],"date-time":"2002-12-22T09:41:38Z","timestamp":1040550098000},"page":"11-28","source":"Crossref","is-referenced-by-count":43,"title":["On Harmonic Weight Enumerators of Binary Codes"],"prefix":"10.1007","volume":"18","author":[{"given":"Christine","family":"Bachoc","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"240905_CR1","unstructured":"C. Bachoc and B. Venkov, Modular forms, lattices and spherical designs, preprint."},{"key":"240905_CR2","unstructured":"A. Bonnecaze, B. Mourrain, and P. Sol\u00e9, Jacobi polynomials, type II codes, and designs, to appear in Designs, Codes and Cryptography."},{"key":"240905_CR3","unstructured":"A. Bonnecaze, E. Rains, and P. Sol\u00e9, 3-colored 5-designs and \u21244-codes, to appear in J. Stat. Inf. and Planning."},{"key":"240905_CR4","unstructured":"A. Bonnecaze, P. Udaya, and P. Sol\u00e9, Strong 4-colored 5-designs, preprint."},{"issue":"1","key":"240905_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0406001","volume":"6","author":"A. R. Calderbank","year":"1993","unstructured":"A. R. Calderbank, and P. Delsarte, On error-correcting codes and invariant linear forms, SIAM J. Disc. Math., Vol. 6,No. 1 (1993) pp. 1-23.","journal-title":"SIAM J. Disc. Math."},{"key":"240905_CR6","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1109\/18.133244","volume":"37","author":"A. R. Calderbank","year":"1991","unstructured":"A. R. Calderbank, P. Delsarte, and N. J. A. Sloane, A strengthening of the Assmus-Mattson theorem, IEEE Trans. Inf. Th., Vol. 37 (1991) pp. 1261-1268.","journal-title":"IEEE Trans. Inf. Th."},{"key":"240905_CR7","doi-asserted-by":"crossref","unstructured":"J. Conway, and N. J. A. Sloane, Sphere packings, Lattices and Groups, Springer-Verlag, (1988).","DOI":"10.1007\/978-1-4757-2016-7"},{"issue":"1","key":"240905_CR8","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1137\/0134012","volume":"34","author":"P. Delsarte","year":"1978","unstructured":"P. Delsarte, Hahn polynomials, discrete harmonics and t-designs, SIAM J. Appl. Math., Vol. 34,No. 1 (1978) pp. 157-166.","journal-title":"SIAM J. Appl. Math."},{"key":"240905_CR9","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF03187604","volume":"6","author":"P. Delsarte","year":"1977","unstructured":"Ph. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geom. Dedicata, Vol. 6 (1977) pp. 363-388.","journal-title":"Geom. Dedicata"},{"key":"240905_CR10","doi-asserted-by":"crossref","unstructured":"W. Ebeling, Lattices and Codes, Vieweg Editor, (1994).","DOI":"10.1007\/978-3-322-96879-1"},{"key":"240905_CR11","unstructured":"J. E. Fields, P. Gaborit, W. C. Huffman, and V. Pless, On the classification of extremal even formally self-dual codes, preprint."},{"key":"240905_CR12","unstructured":"J. E. Fields, P. Gaborit, W. C. Huffman, and V. Pless, On the classification of extremal even formally self-dual codes of length 20 and 22, to appear."},{"key":"240905_CR13","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1023\/A:1008206223659","volume":"11","author":"T. A. Gulliver","year":"1997","unstructured":"T. A. Gulliver, and M. Harada, Classification of extremal double circulant formally self-dual even codes, Designs, Codes and Cryptography, Vol. 11 (1997) pp. 25-35.","journal-title":"Designs, Codes and Cryptography"},{"key":"240905_CR14","unstructured":"G. J. Janusz, Overlap and covering polynomials with applications to designs and self-dual codes, preprint."},{"key":"240905_CR15","first-page":"33","volume":"26","author":"S. Karlin","year":"1961","unstructured":"S. Karlin, and J. McGregor, The Hahn polynomials, formulas and an application, Scripta Math., Vol. 26 (1961) pp. 33-46.","journal-title":"Scripta Math."},{"key":"240905_CR16","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF01388559","volume":"4","author":"G. T. Kennedy","year":"1994","unstructured":"G. T. Kennedy, and V. Pless, On designs and formally self-dual codes, Designs, Codes and Cryptography, Vol. 4 (1994) pp. 43-55.","journal-title":"Designs, Codes and Cryptography"},{"key":"240905_CR17","unstructured":"F. J. MacWilliams, and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland Editor, (1977)."},{"key":"240905_CR18","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1017\/S0305004196001399","volume":"121","author":"M. Ozeki","year":"1997","unstructured":"M. Ozeki, On the notion of Jacobi polynomial for codes, Math. Proc. Camb. Phil. Soc. Vol. 121 (1997) pp. 15-30.","journal-title":"Math. Proc. Camb. Phil. Soc."},{"key":"240905_CR19","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/0012-365X(72)90034-9","volume":"3","author":"V. Pless","year":"1972","unstructured":"V. Pless, A classification of self-orthogonal codes over GF(2), Discrete Math., Vol. 3 (1972) pp. 209-246.","journal-title":"Discrete Math."},{"key":"240905_CR20","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0097-3165(75)90042-4","volume":"18","author":"V. Pless","year":"1975","unstructured":"V. Pless, and N. J. A. Sloane, On the classification and enumeration of self-dual codes, J. Comb. Th. A, Vol. 18 (1975) pp. 313-335.","journal-title":"J. Comb. Th. A"},{"key":"240905_CR21","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF02942571","volume":"68","author":"H.-G. Quebbemann","year":"1998","unstructured":"H.-G. Quebbemann, A shadow identity and an application to isoduality, Abh. Math. Sem. Univ. Hamburg, Vol. 68 (1998) pp. 339-345.","journal-title":"Abh. Math. Sem. Univ. Hamburg"},{"key":"240905_CR22","volume-title":"Handbook of Coding Theory","author":"E. Rains","year":"1998","unstructured":"E. Rains, and N. J. A. Sloane, Self-dual codes, Handbook of Coding Theory, (V. Pless and W. C. Huffman eds.), North Holland, Amsterdam, (1998)."},{"key":"240905_CR23","unstructured":"B. Venkov, R\u00e9seaux et designs sph\u00e9riques, Notes de cours, r\u00e9dig\u00e9es par J. Martinet, to appear"},{"key":"240905_CR24","first-page":"47","volume":"165","author":"B. Venkov","year":"1984","unstructured":"B. Venkov, Even unimodular extremal lattices, Proc. Stecklov Inst. Math., Vol. 165 (1984) pp. 47-52.","journal-title":"Proc. Stecklov Inst. Math."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008368615935.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1008368615935\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008368615935.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T03:34:17Z","timestamp":1753760057000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1008368615935"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,12]]},"references-count":24,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1999,12]]}},"alternative-id":["240905"],"URL":"https:\/\/doi.org\/10.1023\/a:1008368615935","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[1999,12]]}}}