{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T18:09:41Z","timestamp":1771610981238,"version":"3.50.1"},"reference-count":30,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"9","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1321129"],"award-info":[{"award-number":["1321129"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1527524"],"award-info":[{"award-number":["1527524"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1526771"],"award-info":[{"award-number":["1526771"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1109\/tit.2021.3100806","type":"journal-article","created":{"date-parts":[[2021,7,28]],"date-time":"2021-07-28T20:18:25Z","timestamp":1627503505000},"page":"5791-5803","source":"Crossref","is-referenced-by-count":1,"title":["The Birthday Problem and Zero-Error List Codes"],"prefix":"10.1109","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0201-3791","authenticated-orcid":false,"given":"Parham","family":"Noorzad","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3757-0675","authenticated-orcid":false,"given":"Michelle","family":"Effros","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7470-0718","authenticated-orcid":false,"given":"Michael","family":"Langberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2406-7440","authenticated-orcid":false,"given":"Victoria","family":"Kostina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2015.06.037"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/18.720537"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/18.335947"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/18.641560"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.2307\/1401301"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/18.945283"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176991491"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012015"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24676-3_24"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-28628-8_19"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1201\/9781420070033"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579215"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/18.21233"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/0095-8956(82)90002-8","article-title":"Extremals of functions on graphs with applications to graphs and hypergraphs","volume":"32","author":"s\u00f3s","year":"1982","journal-title":"J Combinat Theory B"},{"key":"ref3","author":"cover","year":"2006","journal-title":"Elements of Information Theory"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/18.50381"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-008-0108-3"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/18.61123"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1080\/00031305.1992.10475901","article-title":"A birthday problem solution for nonuniform birth frequencies","volume":"46","author":"nunnikhoven","year":"1992","journal-title":"Amer Statistician"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.2307\/3212893"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"ref9","article-title":"Application of Newton’s identities to a generalized birthday problem and to the Poisson binomial distribution","author":"stein","year":"1990"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1956.1056798"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/11927587_5"},{"key":"ref22","first-page":"547","article-title":"On measures of information and probability","volume":"1","author":"r\u00e9nyi","year":"1961","journal-title":"Proc 4th Berkeley Symp Math Statist Prob"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1090\/dimacs\/020\/08","article-title":"Graph entropy: A survey","volume":"20","author":"simonyi","year":"1995","journal-title":"DIMACS Series in Discrete Mathematics and Theoretical Computer Science"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1965-053-6"},{"key":"ref23","author":"alon","year":"2015","journal-title":"The Probabilistic Method"},{"key":"ref26","first-page":"808","article-title":"Turán’s graph theorem","volume":"102","author":"aigner","year":"1995","journal-title":"Amer Math Monthly"},{"key":"ref25","first-page":"411","article-title":"Coding of an information source having ambiguous alphabet and the entropy of graphs","author":"k\u00f6rner","year":"1973","journal-title":"Proc 6th Prague Conf Inf Theory"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/18\/9523437\/9500216-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/9523437\/09500216.pdf?arnumber=9500216","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T08:10:17Z","timestamp":1725523817000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9500216\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":30,"journal-issue":{"issue":"9"},"URL":"https:\/\/doi.org\/10.1109\/tit.2021.3100806","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9]]}}}