{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:23:12Z","timestamp":1740122592062,"version":"3.37.3"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T00:00:00Z","timestamp":1617667200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T00:00:00Z","timestamp":1617667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["18K03217"],"award-info":[{"award-number":["18K03217"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s10623-021-00874-8","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T20:02:55Z","timestamp":1617739375000},"page":"1241-1254","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Average of complete joint weight enumerators and self-dual codes"],"prefix":"10.1007","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5808-214X","authenticated-orcid":false,"given":"Himadri Shekhar","family":"Chakraborty","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tsuyoshi","family":"Miezaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,6]]},"reference":[{"key":"874_CR1","doi-asserted-by":"publisher","first-page":"2177","DOI":"10.3906\/mat-1905-103","volume":"43","author":"A Bassa","year":"2019","unstructured":"Bassa A., Tutas N.: Extending self-orthogonal codes. Turk. J. Math. 43, 2177\u20132182 (2019).","journal-title":"Turk. J. Math."},{"key":"874_CR2","unstructured":"Chakraborty H.S., Miezaki T.: Variants of Jacobi polynomials in coding theory, in preparation."},{"key":"874_CR3","unstructured":"Chakraborty H.S., Miezaki T., Oura M.: On the cycle index and the weight enumerator II, submitted."},{"issue":"3","key":"874_CR4","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1109\/TIT.1979.1056047","volume":"25","author":"JH Conway","year":"1979","unstructured":"Conway J.H., Pless V.: Self-dual codes over $$GF(3)$$ and $$GF(4)$$ of length not exceeding $$16$$. IEEE Trans. Inf. Theory 25(3), 312\u2013322 (1979).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"874_CR5","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/PL00004225","volume":"11","author":"ST Dougherty","year":"2001","unstructured":"Dougherty S.T., Harada M., Oura M.: Note on the $$g$$-fold joint weight enumerators of self-dual codes over $${\\mathbb{Z}}_k$$. Applicable Algebra Eng. Commun. Comput. 11, 437\u2013445 (2001).","journal-title":"Applicable Algebra Eng. Commun. Comput."},{"key":"874_CR6","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1109\/TIT.1972.1054898","volume":"38","author":"FJ MacWilliams","year":"1972","unstructured":"MacWilliams F.J., Mallows C.L., Conway J.H.: Generalizations of Gleason\u2019s theorem on weight enumerators of self-dual codes. IEEE Trans. Inf. Theory 38, 794\u2013805 (1972).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"874_CR7","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/0097-3165(78)90021-3","volume":"25A","author":"FJ MacWilliams","year":"1978","unstructured":"MacWilliams F.J., Odlyzko A.M., Sloane N.J.A., Ward H.N.: Self-dual codes over GF(4). J. Comb. Theory 25A, 288\u2013318 (1978).","journal-title":"J. Comb. Theory"},{"issue":"6","key":"874_CR8","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1007\/s10623-018-0518-x","volume":"87","author":"T Miezaki","year":"2019","unstructured":"Miezaki T., Oura M.: On the cycle index and the weight enumerator. Des. Codes Cryptogr. 87(6), 1237\u20131242 (2019).","journal-title":"Des. Codes Cryptogr."},{"key":"874_CR9","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0021-9800(68)80067-5","volume":"5","author":"V Pless","year":"1968","unstructured":"Pless V.: On the uniqueness of the Golay codes. J. Comb. Theory 5, 215\u2013228 (1968).","journal-title":"J. Comb. Theory"},{"key":"874_CR10","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/S0019-9958(73)90862-0","volume":"23","author":"V Pless","year":"1973","unstructured":"Pless V., Pierce J.N.: Self-dual codes over $$GF(q)$$ satisfy a modified Varshamov-Gilbert bound. Inf. Control 23, 35\u201340 (1973).","journal-title":"Inf. Control"},{"key":"874_CR11","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1090\/conm\/259\/04118","volume":"259","author":"I Siap","year":"2000","unstructured":"Siap I., Ray-Chaudhuri D.K.: On $$r$$-fold complete weight enumerator of $$r$$ linear codes. Contemp. Math. Am. Math. Soc. 259, 501\u2013513 (2000).","journal-title":"Contemp. Math. Am. Math. Soc."},{"key":"874_CR12","doi-asserted-by":"publisher","first-page":"217","DOI":"10.14492\/hokmj\/1381517759","volume":"18","author":"T Yoshida","year":"1989","unstructured":"Yoshida T.: The average of joint weight enumerators. Hokkaido Math. J. 18, 217\u2013222 (1989).","journal-title":"Hokkaido Math. J."},{"key":"874_CR13","doi-asserted-by":"publisher","first-page":"539","DOI":"10.14492\/hokmj\/1381413988","volume":"20","author":"T Yoshida","year":"1991","unstructured":"Yoshida T.: The average intersection number of a pair of self-dual codes. Hokkaido Math. J. 20, 539\u2013548 (1991).","journal-title":"Hokkaido Math. J."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00874-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-021-00874-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00874-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,26]],"date-time":"2021-05-26T15:24:25Z","timestamp":1622042665000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-021-00874-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,6]]},"references-count":13,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["874"],"URL":"https:\/\/doi.org\/10.1007\/s10623-021-00874-8","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2021,4,6]]},"assertion":[{"value":"25 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}