{"id":"https://openalex.org/W2010696139","doi":"https://doi.org/10.1137/s0895480104444089","title":"Exact Minimum Density of Codes Identifying Vertices in the Square Grid","display_name":"Exact Minimum Density of Codes Identifying Vertices in the Square Grid","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2010696139","doi":"https://doi.org/10.1137/s0895480104444089","mag":"2010696139"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480104444089","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480104444089","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038326851","display_name":"Yael Ben\u2010Haim","orcid":"https://orcid.org/0000-0002-2978-6313"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yael Ben-Haim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044662173","display_name":"Simon Litsyn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simon Litsyn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5132,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.95489493,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"19","issue":"1","first_page":"69","last_page":"82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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":0.9973999857902527,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9944999814033508,"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/vertex","display_name":"Vertex (graph theory)","score":0.7979849576950073},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7881501913070679},{"id":"https://openalex.org/keywords/square-tiling","display_name":"Square tiling","score":0.7612740993499756},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7562580704689026},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.6573131084442139},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.54462069272995},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.4984753131866455},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4735026955604553},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.12482753396034241},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09375190734863281}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7979849576950073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7881501913070679},{"id":"https://openalex.org/C178650486","wikidata":"https://www.wikidata.org/wiki/Q1128619","display_name":"Square tiling","level":3,"score":0.7612740993499756},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7562580704689026},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6573131084442139},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.54462069272995},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4984753131866455},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4735026955604553},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.12482753396034241},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09375190734863281}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895480104444089","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480104444089","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.5591","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.5591","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eng.tau.ac.il/~yael/journal/ID_Codes.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1569855682","https://openalex.org/W1604469657","https://openalex.org/W1688573490","https://openalex.org/W1989117429","https://openalex.org/W2000868891","https://openalex.org/W2038020478","https://openalex.org/W2041065628","https://openalex.org/W2052516832","https://openalex.org/W2065210330","https://openalex.org/W2068361026","https://openalex.org/W2077667712","https://openalex.org/W2084325182","https://openalex.org/W2100994793","https://openalex.org/W2145385305","https://openalex.org/W2149363099","https://openalex.org/W2150169426","https://openalex.org/W2160118466","https://openalex.org/W2162054809","https://openalex.org/W2576165129"],"related_works":["https://openalex.org/W2011928121","https://openalex.org/W4286901735","https://openalex.org/W1999426106","https://openalex.org/W4388906444","https://openalex.org/W2369743165","https://openalex.org/W4302773767","https://openalex.org/W4226107037","https://openalex.org/W281258432","https://openalex.org/W2174875404","https://openalex.org/W2108769088"],"abstract_inverted_index":{"An":[0],"identifying":[1],"code":[2],"C":[3,32,60],"is":[4,42,64],"a":[5,34],"subset":[6],"of":[7,10,24,29,36,49,59],"the":[8,11,17,27,47,56],"vertices":[9],"square":[12],"grid":[13],"${\\mathbb":[14,25,62],"Z}^2$":[15,63],"with":[16],"property":[18],"that":[19,55],"for":[20],"each":[21],"element":[22],"v":[23,41],"Z}^2$,":[26],"collection":[28,48],"elements":[30],"from":[31,40,46],"at":[33,37],"distance":[35],"most":[38],"one":[39],"nonempty":[43],"and":[44],"distinct":[45],"any":[50],"other":[51],"vertex.":[52],"We":[53],"prove":[54],"minimum":[57],"density":[58],"within":[61],"$\\frac{7}{20}$.":[65]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
