{"id":"https://openalex.org/W2149489229","doi":"https://doi.org/10.37236/1720","title":"Binary Gray Codes with Long Bit Runs","display_name":"Binary Gray Codes with Long Bit Runs","publication_year":2003,"publication_date":"2003-06-27","ids":{"openalex":"https://openalex.org/W2149489229","doi":"https://doi.org/10.37236/1720","mag":"2149489229"},"language":"en","primary_location":{"id":"doi:10.37236/1720","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1720","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r27/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r27/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011834415","display_name":"Luis Goddyn","orcid":null},"institutions":[{"id":"https://openalex.org/I122879082","display_name":"Natural Sciences and Engineering Research Council","ror":"https://ror.org/01h531d29","country_code":"CA","type":"government","lineage":["https://openalex.org/I122879082"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Luis Goddyn","raw_affiliation_strings":["Research supported by the Natural Sciences and Engineering Research Council of Canada"],"affiliations":[{"raw_affiliation_string":"Research supported by the Natural Sciences and Engineering Research Council of Canada","institution_ids":["https://openalex.org/I122879082"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018917950","display_name":"Pavol Gvozdjak","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pavol Gvozdjak","raw_affiliation_strings":["Department of Mathematics Simon Fraser University, Burnaby, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Simon Fraser University, Burnaby, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011834415"],"corresponding_institution_ids":["https://openalex.org/I122879082"],"apc_list":null,"apc_paid":null,"fwci":2.3409,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.90205757,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"10","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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":0.9991999864578247,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8068102598190308},{"id":"https://openalex.org/keywords/gray-code","display_name":"Gray code","score":0.7623727321624756},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7358811497688293},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.7251003384590149},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6524286866188049},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5436990857124329},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.4813128709793091},{"id":"https://openalex.org/keywords/gray","display_name":"Gray (unit)","score":0.41951557993888855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4131980538368225},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3576551675796509},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2826763093471527},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.12133258581161499},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.0754111111164093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8068102598190308},{"id":"https://openalex.org/C129861397","wikidata":"https://www.wikidata.org/wiki/Q332772","display_name":"Gray code","level":2,"score":0.7623727321624756},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7358811497688293},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.7251003384590149},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6524286866188049},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5436990857124329},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4813128709793091},{"id":"https://openalex.org/C166275286","wikidata":"https://www.wikidata.org/wiki/Q190095","display_name":"Gray (unit)","level":2,"score":0.41951557993888855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4131980538368225},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3576551675796509},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2826763093471527},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.12133258581161499},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0754111111164093},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/1720","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1720","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r27/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.15.6178","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.6178","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sfu.ca/mast/people/faculty/goddyn/Papers/012-gray-long-bit-runs.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.29.791","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.791","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sfu.ca/~goddyn/Papers/012-gray-long-bit-runs.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.1861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_10/PDF/v10i1r27.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.4.8341","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.8341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_10/PostScriptfiles/v10i1r27.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1720","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1720","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r27/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2149489229.pdf","grobid_xml":"https://content.openalex.org/works/W2149489229.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W93405014","https://openalex.org/W1564007276","https://openalex.org/W2017898591","https://openalex.org/W2046815858","https://openalex.org/W2159193852"],"related_works":["https://openalex.org/W2380005154","https://openalex.org/W2943247777","https://openalex.org/W2619231335","https://openalex.org/W2740543340","https://openalex.org/W2371167013","https://openalex.org/W1582340598","https://openalex.org/W1541021634","https://openalex.org/W2779867339","https://openalex.org/W1997618736","https://openalex.org/W2040688628"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,34,45,68],"there":[3,26],"exists":[4,27],"an":[5],"$n$-bit":[6],"cyclic":[7,29],"binary":[8],"Gray":[9,61],"code":[10],"all":[11],"of":[12,31,55],"whose":[13],"bit":[14,47],"runs":[15],"have":[16],"length":[17],"at":[18],"least":[19],"$n":[20],"-":[21],"3\\log_2":[22],"n$.":[23],"That":[24],"is,":[25],"a":[28],"ordering":[30],"$\\{0,1\\}^n$":[32],"such":[33,44],"adjacent":[35],"words":[36,76],"differ":[37],"in":[38,52,67,77],"exactly":[39],"one":[40],"(coordinate)":[41],"bit,":[42],"and":[43],"no":[46],"changes":[48],"its":[49],"value":[50],"twice":[51],"any":[53],"subsequence":[54],"$n-3\\log_2":[56],"n$":[57],"consecutive":[58],"words.":[59],"Such":[60],"codes":[62],"are":[63],"'locally":[64],"distance":[65,70],"preserving'":[66],"Hamming":[69],"equals":[71],"index":[72],"separation":[73],"for":[74],"nearby":[75],"the":[78],"sequence.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}