{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T06:50:18Z","timestamp":1774680618503,"version":"3.50.1"},"reference-count":42,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"3","license":[{"start":{"date-parts":[[2011,3,1]],"date-time":"2011-03-01T00:00:00Z","timestamp":1298937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. IEEE"],"published-print":{"date-parts":[[2011,3]]},"DOI":"10.1109\/jproc.2010.2095490","type":"journal-article","created":{"date-parts":[[2011,1,31]],"date-time":"2011-01-31T21:08:52Z","timestamp":1296508132000},"page":"388-405","source":"Crossref","is-referenced-by-count":29,"title":["Network Coding and Matroid Theory"],"prefix":"10.1109","volume":"99","author":[{"given":"R","family":"Dougherty","sequence":"first","affiliation":[]},{"given":"C","family":"Freiling","sequence":"additional","affiliation":[]},{"given":"K","family":"Zeger","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref39","first-page":"2116","article-title":"a projection method for derivation of non-shannon-type information inequalities","author":"xu","year":"2008","journal-title":"Proc IEEE Int Symp Inf Theory"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"509","DOI":"10.2307\/2371182","article-title":"On the abstract properties of linear dependence","volume":"57","author":"whitney","year":"1935","journal-title":"Amer J Math"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.907345"},{"key":"ref32","author":"oxley","year":"1992","journal-title":"Matroid Theory"},{"key":"ref31","first-page":"21","article-title":"On coding for non-multicast networks","author":"mdard","year":"2003","journal-title":"Proc 41st Annu Allerton Conf Commun Control Comput"},{"key":"ref30","first-page":"41","article-title":"Infinitely many information inequalities","author":"mat","year":"2007","journal-title":"Proc Int Symp Inf Theory"},{"key":"ref37","year":"1987","journal-title":"Combinatorial Geometries"},{"key":"ref36","author":"welsh","year":"1976","journal-title":"Matroid Theory"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.820015"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2006.261840"},{"key":"ref40","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8608-5","author":"yeung","year":"2002","journal-title":"A First Course in Information Theory"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.896862"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.920209"},{"key":"ref13","author":"dougherty","year":"0","journal-title":"Some achievable rate regions with network coding"},{"key":"ref14","author":"dougherty","year":"0","journal-title":"Non-Shannon information inequalities in four random variables"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.883634"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2048502"},{"key":"ref17","author":"ford","year":"1962","journal-title":"Flows in Networks"},{"key":"ref18","author":"fragouli","year":"2007","journal-title":"Network Coding Fundamentals"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1999.1677"},{"key":"ref4","author":"becker","year":"1993","journal-title":"Grobner Bases A Computational Approach to Commutative Algebra"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.807285"},{"key":"ref27","first-page":"499","article-title":"network information flow: does the model need tuning?","author":"rasala lehman","year":"2005","journal-title":"Proc Symp Discrete Algorithms"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.2307\/2275184"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.864474"},{"key":"ref5","author":"blumenthal","year":"1961","journal-title":"A Modern View of Geometry"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.2307\/2371070"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.851744"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.928963"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/18.850663"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.874405"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1145\/1109557.1109585"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.874531"},{"key":"ref22","first-page":"40","article-title":"On linear network coding","author":"jaggi","year":"2004","journal-title":"Proc 42nd Annu Allerton Conf Commun Control Comput"},{"key":"ref21","first-page":"149","author":"ingleton","year":"1971","journal-title":"Combinatorial Mathematics and its Applications"},{"key":"ref24","article-title":"Network codes as codes on graphs","author":"koetter","year":"2004","journal-title":"38th Annu Conf Inf Sci Syst"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/18.681320"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1561\/0100000007"},{"key":"ref23","article-title":"A duality principle in network coding","author":"koetter","year":"2003","journal-title":"Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) Workshop on Algebraic Coding Theory and Information Theory"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s10922-005-9019-0"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2003.818197"}],"container-title":["Proceedings of the IEEE"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx5\/5\/5715583\/05705535.pdf?arnumber=5705535","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T15:41:54Z","timestamp":1640274114000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/5705535\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":42,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1109\/jproc.2010.2095490","relation":{},"ISSN":["0018-9219","1558-2256"],"issn-type":[{"value":"0018-9219","type":"print"},{"value":"1558-2256","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}