{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:09:57Z","timestamp":1753884597075},"publisher-location":"Berlin, Heidelberg","reference-count":12,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540667230"},{"type":"electronic","value":"9783540467960"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1999]]},"DOI":"10.1007\/3-540-46796-3_44","type":"book-chapter","created":{"date-parts":[[2007,8,2]],"date-time":"2007-08-02T07:14:33Z","timestamp":1186038873000},"page":"462-471","source":"Crossref","is-referenced-by-count":2,"title":["Binary Optimal Linear Rate 1\/2 Codes"],"prefix":"10.1007","author":[{"given":"Koichi","family":"Betsumiya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. Aaron","family":"Gulliver","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masaaki","family":"Harada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2003,5,13]]},"reference":[{"unstructured":"C. Bachoc, On harmonic weight enumerators of binary codes, Designs, Codes and Cryptogr., (to appear).","key":"44_CR1"},{"doi-asserted-by":"crossref","unstructured":"K. Betsumiya, T.A. Gulliver and M. Harada, On binary extremal formally self-dual even codes, Kyushu J. Math. (to appear).","key":"44_CR2","DOI":"10.2206\/kyushujm.53.421"},{"unstructured":"K. Betsumiya and M. Harada, Binary optimal odd formally self-dual codes, (submitted).","key":"44_CR3"},{"key":"44_CR4","first-page":"295","volume-title":"Bounds on the size of linear codes, in Handbook of Coding Theory","author":"A.E. Brouwer","year":"1998","unstructured":"A.E. Brouwer, Bounds on the size of linear codes, in Handbook of Coding Theory, V.S. Pless and W.C. Huffman (Eds.), Elsevier, Amsterdam (1998) pp. 295\u2013461."},{"key":"44_CR5","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1109\/18.59931","volume":"36","author":"J.H. Conway","year":"1990","unstructured":"J.H. Conway and N.J.A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory Vol. 36 (1990) pp. 1319\u20131333.","journal-title":"IEEE Trans. Inform. Theory"},{"doi-asserted-by":"crossref","unstructured":"S.T. Dougherty and M. Harada, Shadow optimal self-dual codes, Kyushu J. Math., (to appear).","key":"44_CR6","DOI":"10.2206\/kyushujm.53.223"},{"unstructured":"J.E. Fields, P. Gaborit, W.C. Huffman and V. Pless, On the classification of extremal even formally self-dual codes, (submitted).","key":"44_CR7"},{"unstructured":"J.E. Fields, P. Gaborit, W.C. Huffman and V. Pless, On the classification of extremal even formally self-dual codes of lengths 20 and 22, (submitted).","key":"44_CR8"},{"key":"44_CR9","doi-asserted-by":"publisher","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 Cryptogr. Vol. 11 (1997) pp. 25\u201335.","journal-title":"Designs, Codes and Cryptogr"},{"unstructured":"D.B. Jaffe, Optimal binary linear codes of length \u2264 30, Discrete Math., (to appear).","key":"44_CR10"},{"key":"44_CR11","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/BF01388559","volume":"4","author":"G. Kennedy","year":"1994","unstructured":"G. Kennedy and V. Pless, On designs and formally self-dual codes, Designs, Codes and Cryptography Vol. 4 (1994) pp. 43\u201355.","journal-title":"Designs, Codes and Cryptography"},{"key":"44_CR12","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1016\/0012-365X(92)90574-Y","volume":"106","author":"J. Simonis","year":"1992","unstructured":"J. Simonis, The [18, 9, 6] code is unique, Discrete Math. Vol. 106\/107 (1992) pp. 439\u2013448.","journal-title":"Discrete Math"}],"container-title":["Lecture Notes in Computer Science","Applied Algebra, Algebraic Algorithms and Error-Correcting Codes"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-46796-3_44","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,17]],"date-time":"2019-02-17T16:49:12Z","timestamp":1550422152000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-46796-3_44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999]]},"ISBN":["9783540667230","9783540467960"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/3-540-46796-3_44","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[1999]]}}}