乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:10:26Z","timestamp":1709251826240},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T00:00:00Z","timestamp":1699920000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T00:00:00Z","timestamp":1699920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Australian Research Council Centre of Excellence for Plant Success in Nature & Agriculture","award":["CE200100015"]},{"name":"The Scientific and Technological Research Council of Turkey","award":["TUBITAK 121F111"]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2024,2]]},"abstract":"Abstract<\/jats:title>A lower bound is presented for the minimal number of filled cells in a maximal partial Latin hypercube of dimension d<\/jats:italic> and order n<\/jats:italic>. The result generalises and extends previous results for

$$d=2$$<\/jats:tex-math>\n \n d<\/mml:mi>\n =<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (Latin squares) and

$$d=3$$<\/jats:tex-math>\n \n d<\/mml:mi>\n =<\/mml:mo>\n 3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (Latin cubes). Explicit constructions show that this bound is near-optimal for large

$$n> d$$<\/jats:tex-math>\n \n n<\/mml:mi>\n ><\/mml:mo>\n d<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. For

$$d>n$$<\/jats:tex-math>\n \n d<\/mml:mi>\n ><\/mml:mo>\n n<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, a connection with Hamming codes shows that this lower bound gives a related upper bound for the same quantity. The results can be interpreted in terms of independent dominating sets in certain graphs, and in terms of codes that have covering radius 1 and minimum distance at least 2.<\/jats:p>","DOI":"10.1007\/s10623-023-01314-5","type":"journal-article","created":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T13:02:49Z","timestamp":1699966969000},"page":"419-433","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On maximal partial Latin hypercubes"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-1329-3514","authenticated-orcid":false,"given":"Diane M.","family":"Donovan","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0429-0493","authenticated-orcid":false,"given":"Mike J.","family":"Grannell","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6824-451X","authenticated-orcid":false,"given":"Emine \u015eule","family":"Yaz\u0131c\u0131","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,11,14]]},"reference":[{"issue":"1\u20134","key":"1314_CR1","first-page":"31","volume":"65","author":"S Arumugam","year":"1998","unstructured":"Arumugam S., Kala R.: Domination parameters of hypercubes. 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Codes Cryptogr."},{"issue":"2","key":"1314_CR10","first-page":"601","volume":"41","author":"J Quistorff","year":"2001","unstructured":"Quistorff J.: On codes with given minimum distance and covering radius. Beitr\u00e4ge Algebra Geom. 41(2), 601\u2013611 (2001).","journal-title":"Beitr\u00e4ge Algebra Geom."},{"key":"1314_CR11","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/S0021-9800(70)80018-7","volume":"9","author":"ER Rodemich","year":"1970","unstructured":"Rodemich E.R.: Coverings by rook domains. J. Comb. Theory 9, 117\u2013128 (1970).","journal-title":"J. Comb. Theory"},{"key":"1314_CR12","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1112\/jlms\/s2-1.1.493","volume":"1","author":"RG Stanton","year":"1969","unstructured":"Stanton R.G., Horton J.D., Kalbfleisch J.G.: Covering theorems for vectors with special reference to the case of four and five components. J. Lond. Math. Soc. 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