{"id":"https://openalex.org/W7117309888","doi":"https://doi.org/10.1109/tit.2025.3648920","title":"Bounds on <i>k</i> -Hash Distances and Rates of Linear Codes","display_name":"Bounds on <i>k</i> -Hash Distances and Rates of Linear Codes","publication_year":2025,"publication_date":"2025-12-26","ids":{"openalex":"https://openalex.org/W7117309888","doi":"https://doi.org/10.1109/tit.2025.3648920"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2025.3648920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3648920","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":"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/A5041359704","display_name":"Stefano Della Fiore","orcid":"https://orcid.org/0000-0002-7034-084X"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Della Fiore","raw_affiliation_strings":["Department of Information Engineering, University of Brescia, Brescia, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7034-084X","affiliations":[{"raw_affiliation_string":"Department of Information Engineering, University of Brescia, Brescia, Italy","institution_ids":["https://openalex.org/I79940851"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037433671","display_name":"Marco Dalai","orcid":"https://orcid.org/0000-0003-2132-7072"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Dalai","raw_affiliation_strings":["Department of Information Engineering, University of Brescia, Brescia, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2132-7072","affiliations":[{"raw_affiliation_string":"Department of Information Engineering, University of Brescia, Brescia, Italy","institution_ids":["https://openalex.org/I79940851"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I79940851"],"apc_list":null,"apc_paid":null,"fwci":1.2282,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.88466252,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"72","issue":"2","first_page":"865","last_page":"875"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.35370001196861267,"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":0.35370001196861267,"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":0.20280000567436218,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.188400000333786,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48410001397132874},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.44130000472068787},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.42669999599456787},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.42640000581741333},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.42579999566078186},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.3898000121116638},{"id":"https://openalex.org/keywords/channel-code","display_name":"Channel code","score":0.33970001339912415}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6237000226974487},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5439000129699707},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48410001397132874},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.44130000472068787},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.42669999599456787},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42579999566078186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42340001463890076},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3898000121116638},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34940001368522644},{"id":"https://openalex.org/C166366890","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Channel code","level":3,"score":0.33970001339912415},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.2906999886035919},{"id":"https://openalex.org/C206468330","wikidata":"https://www.wikidata.org/wiki/Q834373","display_name":"Code rate","level":3,"score":0.2858999967575073},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25380000472068787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3648920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3648920","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1911679041","https://openalex.org/W1971836973","https://openalex.org/W1980392009","https://openalex.org/W1987789009","https://openalex.org/W1997218732","https://openalex.org/W2034215849","https://openalex.org/W2053816258","https://openalex.org/W2056884477","https://openalex.org/W2078289947","https://openalex.org/W2092976320","https://openalex.org/W2099111195","https://openalex.org/W2109084006","https://openalex.org/W2134687114","https://openalex.org/W2148695545","https://openalex.org/W2485226336","https://openalex.org/W2965885331","https://openalex.org/W3099842202","https://openalex.org/W3157485528","https://openalex.org/W3158439805","https://openalex.org/W3198613070","https://openalex.org/W3199899104","https://openalex.org/W4205759049","https://openalex.org/W4220790181","https://openalex.org/W4239602426","https://openalex.org/W4367669913","https://openalex.org/W4391631025","https://openalex.org/W4399051511","https://openalex.org/W4405558440"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,30],"bound":[4],"the":[5,12,24,38,42,58],"rate":[6],"of":[7,26,37,62],"linear":[8],"codes":[9],"in":[10,20,41],"Fnqwith":[11],"property":[13],"that":[14],"anyk\u2264qcodewords":[15],"are":[16],"all":[17],"simultaneously":[18],"distinct":[19],"at":[21],"leastdkcoordinates.":[22],"For":[23],"case":[25],"particular":[27],"interestq=k=":[28],"3":[29],"recover,":[31],"with":[32],"a":[33],"simpler":[34],"proof,":[35],"state":[36],"art":[39],"results":[40],"cased3=":[43],"1":[44],"and":[45],"new":[46],"bounds":[47],"ford3>":[48],"1.":[49],"We":[50],"finally":[51],"discuss":[52],"some":[53],"related":[54],"open":[55],"problems":[56],"on":[57],"list-decoding":[59],"zero-error":[60],"capacity":[61],"discrete":[63],"memoryless":[64],"channels.":[65]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-12-26T00:00:00"}