{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T09:54:22Z","timestamp":1740131662021,"version":"3.37.3"},"reference-count":45,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"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","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":[[2019,1]]},"DOI":"10.1109\/tit.2018.2866244","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T19:02:25Z","timestamp":1534878145000},"page":"220-234","source":"Crossref","is-referenced-by-count":4,"title":["Capacity and Achievable Rate Regions for Linear Network Coding Over Ring Alphabets"],"prefix":"10.1109","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7307-7023","authenticated-orcid":false,"given":"Joseph","family":"Connelly","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6415-1447","authenticated-orcid":false,"given":"Kenneth","family":"Zeger","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2473863"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.2016.2613085"},{"journal-title":"Linear Algebra over Commutative Rings","year":"1984","author":"mcdonald","key":"ref33"},{"journal-title":"Finite Rings with Identity","year":"1974","author":"mcdonald","key":"ref32"},{"key":"ref31","first-page":"1","article-title":"Linear codes cannot approximate the network capacity within any constant factor","volume":"21","author":"lovett","year":"2014","journal-title":"Electronic Colloq on Computational Complexity"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2010.2093851"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2613988"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.820015"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2555955"},{"key":"ref34","first-page":"1","article-title":"On coding for non-multicast networks","author":"m\u00e9dard","year":"2003","journal-title":"Proc Conf Commun Contr Comput"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1049\/iet-net.2016.0094"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.2014.2350982"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.851744"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.874405"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.896862"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2403315"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2403361"},{"journal-title":"Abstract Algebra","year":"2004","author":"dummit","key":"ref16"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2094930"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/NETCOD.2014.6892127"},{"journal-title":"Abstract Algebra","year":"2007","author":"grillet","key":"ref19"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2094910"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.864474"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8616-0"},{"journal-title":"Matrices over Commutative Rings","year":"1992","author":"brown","key":"ref3"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2334291"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.807285"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.928963"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2697421"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2618379"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2011.39"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2697422"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/18.850663"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2009.05.029"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2553676"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.881746"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.874531"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2014.6875214"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2013.2270438"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/Allerton.2013.6736710"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/18.641556"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2628797"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2201340"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.847712"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielaam\/18\/8581519\/8443369-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/8581519\/08443369.pdf?arnumber=8443369","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,13]],"date-time":"2022-07-13T21:09:00Z","timestamp":1657746540000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8443369\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":45,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/tit.2018.2866244","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"type":"print","value":"0018-9448"},{"type":"electronic","value":"1557-9654"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}