{"id":"https://openalex.org/W2093127356","doi":"https://doi.org/10.1109/isit.2014.6875415","title":"Families of Optimal Binary Non-MDS Erasure Codes","display_name":"Families of Optimal Binary Non-MDS Erasure Codes","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2093127356","doi":"https://doi.org/10.1109/isit.2014.6875415","mag":"2093127356"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2014.6875415","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2014.6875415","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1609.02460","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011632840","display_name":"Danilo Gligoroski","orcid":"https://orcid.org/0000-0002-7078-6139"},"institutions":[{"id":"https://openalex.org/I4210105718","display_name":"Trondheim Kommune","ror":"https://ror.org/01gjtys23","country_code":"NO","type":"government","lineage":["https://openalex.org/I4210105718"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Danilo Gligoroski","raw_affiliation_strings":["Norges teknisk-naturvitenskapelige universitet, Trondheim, NO"],"affiliations":[{"raw_affiliation_string":"Norges teknisk-naturvitenskapelige universitet, Trondheim, NO","institution_ids":["https://openalex.org/I4210105718"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064365516","display_name":"Katina Kralevska","orcid":"https://orcid.org/0009-0009-0603-8310"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Katina Kralevska","raw_affiliation_strings":["Department of Telematics, Norwegian University of Science and Technology, Trondheim, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Telematics, Norwegian University of Science and Technology, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011632840"],"corresponding_institution_ids":["https://openalex.org/I4210105718"],"apc_list":null,"apc_paid":null,"fwci":0.7238,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.76811629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"3150","last_page":"3154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9995999932289124,"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":0.9995999932289124,"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/T11130","display_name":"Coding theory and cryptography","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.7094919085502625},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6244628429412842},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5504291653633118},{"id":"https://openalex.org/keywords/tornado-code","display_name":"Tornado code","score":0.515270471572876},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.4836174547672272},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4749729037284851},{"id":"https://openalex.org/keywords/luby-transform-code","display_name":"Luby transform code","score":0.4724367558956146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4690454602241516},{"id":"https://openalex.org/keywords/binary-erasure-channel","display_name":"Binary erasure channel","score":0.4638279676437378},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.46124759316444397},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.46101701259613037},{"id":"https://openalex.org/keywords/erasure-code","display_name":"Erasure code","score":0.4585939943790436},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.45385441184043884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45105257630348206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4475046396255493},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.43729543685913086},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37027519941329956},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.32639408111572266},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2381097972393036},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08844605088233948},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.08502283692359924},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.05042794346809387}],"concepts":[{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.7094919085502625},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6244628429412842},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5504291653633118},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.515270471572876},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.4836174547672272},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4749729037284851},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.4724367558956146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4690454602241516},{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.4638279676437378},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.46124759316444397},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.46101701259613037},{"id":"https://openalex.org/C137529215","wikidata":"https://www.wikidata.org/wiki/Q5385031","display_name":"Erasure code","level":3,"score":0.4585939943790436},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.45385441184043884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45105257630348206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4475046396255493},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.43729543685913086},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37027519941329956},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.32639408111572266},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2381097972393036},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08844605088233948},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.08502283692359924},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.05042794346809387},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2014.6875415","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2014.6875415","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1609.02460","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.02460","pdf_url":"https://arxiv.org/pdf/1609.02460","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:1609.02460","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.02460","pdf_url":"https://arxiv.org/pdf/1609.02460","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W330091898","https://openalex.org/W1513529697","https://openalex.org/W1530125006","https://openalex.org/W1537045696","https://openalex.org/W1606480398","https://openalex.org/W1622719107","https://openalex.org/W2012785774","https://openalex.org/W2014475896","https://openalex.org/W2029712200","https://openalex.org/W2048235391","https://openalex.org/W2051526677","https://openalex.org/W2080242564","https://openalex.org/W2099837838","https://openalex.org/W2105831729","https://openalex.org/W2111072216","https://openalex.org/W2137266817","https://openalex.org/W2146397633","https://openalex.org/W2147343704","https://openalex.org/W2147527217","https://openalex.org/W2148575324","https://openalex.org/W2163729038","https://openalex.org/W2163775180","https://openalex.org/W2168760966","https://openalex.org/W2235016025","https://openalex.org/W2623293810","https://openalex.org/W2963480020","https://openalex.org/W4239704585","https://openalex.org/W6611419579","https://openalex.org/W6630477653","https://openalex.org/W6632200215","https://openalex.org/W6636645890","https://openalex.org/W6682296083"],"related_works":["https://openalex.org/W1985033232","https://openalex.org/W1983975287","https://openalex.org/W2363930252","https://openalex.org/W3007776233","https://openalex.org/W1971149437","https://openalex.org/W2053950481","https://openalex.org/W2149057203","https://openalex.org/W2162141500","https://openalex.org/W2744779861","https://openalex.org/W2604463289"],"abstract_inverted_index":{"We":[0,66],"introduce":[1],"a":[2,55,69],"definition":[3],"for":[4,12,22,73],"Families":[5],"of":[6,43,76,81,93],"Optimal":[7],"Binary":[8],"Non-MDS":[9],"Erasure":[10],"Codes":[11],"[n,":[13],"k]":[14],"codes":[15,44,52,83,95],"over":[16,31],"GF(2),":[17],"and":[18],"propose":[19],"an":[20],"algorithm":[21],"finding":[23],"those":[24,41],"families":[25,42],"by":[26,97],"using":[27],"hill":[28,38],"climbing":[29,39],"techniques":[30],"Balanced":[32],"XOR":[33],"codes.":[34,65],"Due":[35],"to":[36,89],"the":[37,51,78,90,94,104],"search,":[40],"have":[45],"always":[46],"better":[47],"decoding":[48,79,91],"probability":[49,80,92],"than":[50],"generated":[53],"in":[54,84,103],"typical":[56],"Random":[57,98],"Linear":[58,99],"Network":[59,100],"Coding":[60,101],"scenario,":[61],"i.e.,":[62],"random":[63],"linear":[64],"also":[67],"show":[68],"surprising":[70],"result":[71],"that":[72],"small":[74],"values":[75],"k,":[77],"our":[82],"GF(2)":[85],"is":[86],"very":[87],"close":[88],"obtained":[96],"but":[102],"higher":[105],"finite":[106],"field":[107],"GF(4).":[108]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}