{"id":"https://openalex.org/W2976892179","doi":"https://doi.org/10.1109/isit.2019.8849486","title":"Unrestricted Generalized Column Distances: A Wider Definition","display_name":"Unrestricted Generalized Column Distances: A Wider Definition","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2976892179","doi":"https://doi.org/10.1109/isit.2019.8849486","mag":"2976892179"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849486","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5078831117","display_name":"Sara D. Cardell","orcid":"https://orcid.org/0000-0003-0225-5106"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Sara D. Cardell","raw_affiliation_strings":["Imecc, University of Campinas, Brazil"],"affiliations":[{"raw_affiliation_string":"Imecc, University of Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026023196","display_name":"Diego Napp","orcid":"https://orcid.org/0000-0003-2303-9824"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Diego Napp","raw_affiliation_strings":["DM, University of Alicante, Spain"],"affiliations":[{"raw_affiliation_string":"DM, University of Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062307376","display_name":"Marcelo Firer","orcid":"https://orcid.org/0000-0001-6887-7683"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marcelo Firer","raw_affiliation_strings":["Imecc, University of Campinas, Brazil"],"affiliations":[{"raw_affiliation_string":"Imecc, University of Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078831117"],"corresponding_institution_ids":["https://openalex.org/I181391015"],"apc_list":null,"apc_paid":null,"fwci":0.1446,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.58534003,"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":"2783","last_page":"2787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"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/hamming-distance","display_name":"Hamming distance","score":0.585745096206665},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.5792116522789001},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.5425740480422974},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.5298476219177246},{"id":"https://openalex.org/keywords/convolutional-code","display_name":"Convolutional code","score":0.5171384215354919},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.5096204280853271},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49100449681282043},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4857252240180969},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.45430949330329895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44357407093048096},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4404798448085785},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4132336378097534},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35233715176582336},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3248322606086731},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1842854917049408},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.13390305638313293},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06150200963020325}],"concepts":[{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.585745096206665},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.5792116522789001},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.5425740480422974},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.5298476219177246},{"id":"https://openalex.org/C157899210","wikidata":"https://www.wikidata.org/wiki/Q1395022","display_name":"Convolutional code","level":3,"score":0.5171384215354919},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.5096204280853271},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49100449681282043},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4857252240180969},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.45430949330329895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44357407093048096},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4404798448085785},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4132336378097534},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35233715176582336},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3248322606086731},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1842854917049408},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.13390305638313293},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06150200963020325},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2019.8849486","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1521126234","https://openalex.org/W1530125006","https://openalex.org/W1606480398","https://openalex.org/W1836967236","https://openalex.org/W1989721338","https://openalex.org/W2012785774","https://openalex.org/W2019771491","https://openalex.org/W2034347399","https://openalex.org/W2041788275","https://openalex.org/W2050338340","https://openalex.org/W2078990321","https://openalex.org/W2092667913","https://openalex.org/W2095978440","https://openalex.org/W2097117337","https://openalex.org/W2102336264","https://openalex.org/W2111616448","https://openalex.org/W2127558904","https://openalex.org/W2147092309","https://openalex.org/W2152220451","https://openalex.org/W2157587788","https://openalex.org/W2162013214","https://openalex.org/W2171283709","https://openalex.org/W2346940528","https://openalex.org/W2616592276","https://openalex.org/W2745045861","https://openalex.org/W2895335898","https://openalex.org/W2963900659","https://openalex.org/W2963992030","https://openalex.org/W2964317418","https://openalex.org/W3104563927","https://openalex.org/W4234444615","https://openalex.org/W4239704585","https://openalex.org/W4242536966","https://openalex.org/W4247189741","https://openalex.org/W6660796629","https://openalex.org/W6674884959","https://openalex.org/W6683695819"],"related_works":["https://openalex.org/W2134357506","https://openalex.org/W1916643713","https://openalex.org/W2138557067","https://openalex.org/W3045580795","https://openalex.org/W2949538461","https://openalex.org/W2164611661","https://openalex.org/W2357428230","https://openalex.org/W2160208418","https://openalex.org/W2976892179","https://openalex.org/W3034594523"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3],"introduce":[4],"the":[5,18,22,32],"concept":[6,19],"of":[7,34,45,60],"Unrestricted":[8],"Generalized":[9],"Column":[10],"Distance":[11],"(UGCD)":[12],"for":[13,26],"convolutional":[14],"codes.":[15,28],"This":[16],"is":[17,36],"equivalent":[20],"to":[21,42,56],"generalized":[23],"Hamming":[24],"weights":[25],"block":[27],"We":[29,51],"show":[30,40],"that":[31],"hierarchy":[33],"UGCD":[35],"strictly":[37],"increasing":[38],"and":[39],"how":[41],"compute":[43,57],"it":[44,58],"parity-check":[46,63],"matrix":[47],"in":[48],"general":[49],"form.":[50],"also":[52],"provide":[53],"a":[54,61],"way":[55],"out":[59],"systematic":[62],"matrix.":[64]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-14T06:41:57.775601","created_date":"2025-10-10T00:00:00"}