{"id":"https://openalex.org/W2018383088","doi":"https://doi.org/10.1109/tit.2013.2286616","title":"Gray Codes and Enumerative Coding for Vector Spaces","display_name":"Gray Codes and Enumerative Coding for Vector Spaces","publication_year":2013,"publication_date":"2013-10-21","ids":{"openalex":"https://openalex.org/W2018383088","doi":"https://doi.org/10.1109/tit.2013.2286616","mag":"2018383088"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2286616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2286616","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1305.5765","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054043026","display_name":"Moshe Schwartz","orcid":"https://orcid.org/0000-0002-1449-0026"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Moshe Schwartz","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel","Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054043026"],"corresponding_institution_ids":["https://openalex.org/I124227911"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11324354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"1","first_page":"271","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9916999936103821,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.6858958005905151},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5503619313240051},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5278147459030151},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.506683886051178},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40716007351875305},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.40561360120773315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35468125343322754},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35073429346084595},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3323485255241394},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11054772138595581}],"concepts":[{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.6858958005905151},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5503619313240051},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5278147459030151},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.506683886051178},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40716007351875305},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40561360120773315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35468125343322754},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35073429346084595},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3323485255241394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11054772138595581}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2013.2286616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2286616","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:1305.5765","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1305.5765","pdf_url":"https://arxiv.org/pdf/1305.5765","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":"","raw_type":"text"},{"id":"mag:2018383088","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1305.5765.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.746.1326","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.746.1326","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1305.5765.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1305.5765","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1305.5765","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1305.5765","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1305.5765","pdf_url":"https://arxiv.org/pdf/1305.5765","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018383088.pdf","grobid_xml":"https://content.openalex.org/works/W2018383088.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W93405014","https://openalex.org/W1568510176","https://openalex.org/W1973288683","https://openalex.org/W1976090498","https://openalex.org/W1979021998","https://openalex.org/W1981663184","https://openalex.org/W1996897280","https://openalex.org/W2034323860","https://openalex.org/W2046815858","https://openalex.org/W2049675484","https://openalex.org/W2049948530","https://openalex.org/W2055060019","https://openalex.org/W2060454056","https://openalex.org/W2068050433","https://openalex.org/W2076639947","https://openalex.org/W2087957223","https://openalex.org/W2088742261","https://openalex.org/W2095418648","https://openalex.org/W2098313715","https://openalex.org/W2128555802","https://openalex.org/W2130908226","https://openalex.org/W2139145447","https://openalex.org/W2139416652","https://openalex.org/W2149434632","https://openalex.org/W2155398259","https://openalex.org/W2156683452","https://openalex.org/W2158464899","https://openalex.org/W2159338688","https://openalex.org/W2167137513","https://openalex.org/W2170835539","https://openalex.org/W2295821770","https://openalex.org/W2570004196","https://openalex.org/W2952958801","https://openalex.org/W2953315799","https://openalex.org/W3101800757","https://openalex.org/W4232038591","https://openalex.org/W4233121052"],"related_works":["https://openalex.org/W2963856035","https://openalex.org/W2146523743","https://openalex.org/W2920965311","https://openalex.org/W2782962908","https://openalex.org/W2951134075","https://openalex.org/W2342662384","https://openalex.org/W1806796113","https://openalex.org/W1975802705","https://openalex.org/W2139584447","https://openalex.org/W3036797629","https://openalex.org/W2071383517","https://openalex.org/W3173907454","https://openalex.org/W2964936392","https://openalex.org/W2996995381","https://openalex.org/W657059770","https://openalex.org/W2086120244","https://openalex.org/W3016614437","https://openalex.org/W2544856930","https://openalex.org/W2964235003","https://openalex.org/W3106347320"],"abstract_inverted_index":{"Gray":[0,68],"codes":[1,35],"for":[2,38,42,48,65,90],"vector":[3],"spaces":[4],"are":[5,36,51,63],"considered":[6],"in":[7,24],"two":[8,46],"graphs:":[9],"the":[10,14,28,43,66,79,94],"Grassmann":[11,29],"graph,":[12,16,30,45],"and":[13,60,89],"projective-space":[15,44],"both":[17],"of":[18,32,78],"which":[19,70],"have":[20],"recently":[21],"found":[22],"applications":[23],"network":[25],"coding.":[26],"For":[27],"constructions":[31,47],"cyclic":[33],"optimal":[34],"given":[37,64],"all":[39],"parameters.":[40],"As":[41],"specific":[49],"parameters":[50],"provided,":[52],"as":[53,84,86],"well":[54],"some":[55],"non-existence":[56],"results.":[57],"Furthermore,":[58],"encoding":[59],"decoding":[61],"algorithms":[62,80],"Grassmannian":[67],"code,":[69],"induce":[71],"an":[72],"enumerative-coding":[73],"scheme.":[74],"The":[75],"computational":[76],"complexity":[77],"is":[81],"at":[82],"least":[83],"low":[85],"known":[87],"schemes,":[88],"certain":[91],"parameter":[92],"ranges,":[93],"new":[95],"scheme":[96],"outperforms":[97],"previously-known":[98],"ones.":[99]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
