{"id":"https://openalex.org/W2532691608","doi":"https://doi.org/10.1109/tit.2016.2618379","title":"A Class of Non-Linearly Solvable Networks","display_name":"A Class of Non-Linearly Solvable Networks","publication_year":2016,"publication_date":"2016-10-19","ids":{"openalex":"https://openalex.org/W2532691608","doi":"https://doi.org/10.1109/tit.2016.2618379","mag":"2532691608"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2618379","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2618379","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.03803","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082875389","display_name":"Joseph Connelly","orcid":"https://orcid.org/0000-0001-7307-7023"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joseph Connelly","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072111370","display_name":"K. Zeger","orcid":"https://orcid.org/0000-0001-6415-1447"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth Zeger","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082875389"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":2.4294,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.90236546,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"63","issue":"1","first_page":"201","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.780343234539032},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7479361295700073},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7130529880523682},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6351236701011658},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5741851329803467},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.565131425857544},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5293999910354614},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5173355937004089},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4760803282260895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4465941786766052},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1835620105266571},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1316310465335846},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08634486794471741}],"concepts":[{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.780343234539032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7479361295700073},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7130529880523682},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6351236701011658},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5741851329803467},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.565131425857544},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5293999910354614},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5173355937004089},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4760803282260895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4465941786766052},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1835620105266571},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1316310465335846},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08634486794471741},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2016.2618379","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2618379","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1601.03803","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.03803","pdf_url":"https://arxiv.org/pdf/1601.03803","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.03803","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.03803","pdf_url":"https://arxiv.org/pdf/1601.03803","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2532691608.pdf","grobid_xml":"https://content.openalex.org/works/W2532691608.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W110310473","https://openalex.org/W593489687","https://openalex.org/W1483151078","https://openalex.org/W1757164770","https://openalex.org/W1804057676","https://openalex.org/W1939076699","https://openalex.org/W1982709858","https://openalex.org/W2016444590","https://openalex.org/W2026482663","https://openalex.org/W2028078858","https://openalex.org/W2035908129","https://openalex.org/W2039708723","https://openalex.org/W2081008934","https://openalex.org/W2090929931","https://openalex.org/W2103320637","https://openalex.org/W2104389845","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2114578240","https://openalex.org/W2130512442","https://openalex.org/W2132123317","https://openalex.org/W2138928022","https://openalex.org/W2147664948","https://openalex.org/W2150284816","https://openalex.org/W2159572035","https://openalex.org/W2167703619","https://openalex.org/W2171844485","https://openalex.org/W2212571888","https://openalex.org/W2264615359","https://openalex.org/W2561436563","https://openalex.org/W2567286734","https://openalex.org/W2571300684","https://openalex.org/W2963428994","https://openalex.org/W2963430405","https://openalex.org/W3098321199","https://openalex.org/W3101064986","https://openalex.org/W3104866025","https://openalex.org/W3112909250","https://openalex.org/W3126588943","https://openalex.org/W3158755844","https://openalex.org/W4238145030","https://openalex.org/W6604565194"],"related_works":["https://openalex.org/W2074481494","https://openalex.org/W4250156143","https://openalex.org/W3013085049","https://openalex.org/W4247156967","https://openalex.org/W4239207432","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W2777710427","https://openalex.org/W4299961354","https://openalex.org/W1955455432"],"abstract_inverted_index":{"For":[0],"each":[1],"positive":[2],"composite":[3,80],"integer":[4],"m,":[5],"a":[6,78,84],"network":[7,85],"is":[8,11,20,77,86],"constructed,":[9],"which":[10],"solvable":[12,22,42,88],"over":[13,23,33,43,89],"an":[14],"alphabet":[15],"of":[16],"size":[17],"m":[18,76],"but":[19],"not":[21,39,87],"any":[24,34,44,90],"smaller":[25],"alphabet.":[26,92],"These":[27],"networks":[28],"have":[29],"no":[30],"linear":[31,58],"solutions":[32],"module":[35],"alphabets":[36],"and":[37,56],"are":[38,50,60],"asymptotically":[40],"linearly":[41],"finite-field":[45,71],"alphabets.":[46,72],"The":[47],"networks'":[48],"capacities":[49,59],"all":[51,61,70],"shown":[52,62],"to":[53,63],"equal":[54],"one,":[55],"their":[57],"be":[64],"bounded":[65],"away":[66],"from":[67],"one":[68],"for":[69],"In":[73],"addition,":[74],"if":[75],"non-power-of-prime":[79],"number,":[81],"then":[82],"such":[83],"prime-power-size":[91]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}