{"id":"https://openalex.org/W2962919236","doi":"https://doi.org/10.1109/cig.2010.5592743","title":"Dense error-correcting codes in the Lee metric","display_name":"Dense error-correcting codes in the Lee metric","publication_year":2010,"publication_date":"2010-08-01","ids":{"openalex":"https://openalex.org/W2962919236","doi":"https://doi.org/10.1109/cig.2010.5592743","mag":"2962919236"},"language":"en","primary_location":{"id":"doi:10.1109/cig.2010.5592743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cig.2010.5592743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Information Theory Workshop","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/A5097348508","display_name":"Tuvi Etzi","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Tuvi Etzi","raw_affiliation_strings":["Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004102644","display_name":"Alexander Vardy","orcid":"https://orcid.org/0000-0003-3303-9078"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Vardy","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021586372","display_name":"Eitan Yaakobi","orcid":"https://orcid.org/0000-0002-9851-5234"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eitan Yaakobi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5097348508"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.8823,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.79528905,"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":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"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/T11130","display_name":"Coding theory and cryptography","score":0.9973999857902527,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9972000122070312,"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/block-code","display_name":"Block code","score":0.6353342533111572},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5760012269020081},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.5166121125221252},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5058678984642029},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4994502067565918},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.49049848318099976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.475910484790802},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.47233548760414124},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.4660210609436035},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4266315996646881},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40784716606140137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38306325674057007},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1631775200366974}],"concepts":[{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.6353342533111572},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5760012269020081},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.5166121125221252},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5058678984642029},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4994502067565918},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.49049848318099976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.475910484790802},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.47233548760414124},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.4660210609436035},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4266315996646881},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40784716606140137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38306325674057007},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1631775200366974},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cig.2010.5592743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cig.2010.5592743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Information Theory Workshop","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W33658691","https://openalex.org/W33833956","https://openalex.org/W109405981","https://openalex.org/W1521447642","https://openalex.org/W1584248758","https://openalex.org/W1606480398","https://openalex.org/W1640881979","https://openalex.org/W1968886440","https://openalex.org/W1990315714","https://openalex.org/W1992472342","https://openalex.org/W2009331731","https://openalex.org/W2018968136","https://openalex.org/W2029946422","https://openalex.org/W2040989249","https://openalex.org/W2044492449","https://openalex.org/W2070938277","https://openalex.org/W2076760134","https://openalex.org/W2081408407","https://openalex.org/W2093668230","https://openalex.org/W2104885095","https://openalex.org/W2107415712","https://openalex.org/W2115545375","https://openalex.org/W2121567355","https://openalex.org/W2128970384","https://openalex.org/W2130752227","https://openalex.org/W2132083478","https://openalex.org/W2163962630","https://openalex.org/W2166966427","https://openalex.org/W2800924487","https://openalex.org/W2895239415","https://openalex.org/W3041682493","https://openalex.org/W3101163237","https://openalex.org/W4285719527","https://openalex.org/W6604469142","https://openalex.org/W6679144576","https://openalex.org/W6751009815","https://openalex.org/W6781063283"],"related_works":["https://openalex.org/W1968396483","https://openalex.org/W4297536019","https://openalex.org/W1509734363","https://openalex.org/W135568846","https://openalex.org/W2913933112","https://openalex.org/W2950636389","https://openalex.org/W2150212378","https://openalex.org/W2121825730","https://openalex.org/W2172754641","https://openalex.org/W2731597386"],"abstract_inverted_index":{"Several":[0],"new":[1,7],"applications":[2],"and":[3,33,80,146],"a":[4,97,105],"number":[5],"of":[6,35,46,64,124,157],"mathematical":[8],"techniques":[9],"have":[10],"increased":[11],"the":[12,18,22,39,100,116,137,150],"research":[13],"on":[14,127],"error-correcting":[15,36,48],"codes":[16,37,49,67,76,125,135,153],"in":[17,21,38,50,104,115],"Lee":[19,40,91],"metric":[20],"last":[23],"decade.":[24],"In":[25],"this":[26],"work":[27],"we":[28,43,60],"consider":[29,44],"several":[30],"coding":[31],"problems":[32],"constructions":[34,45],"metric.":[41],"First,":[42],"dense":[47],"relatively":[51,106],"small":[52,55,107],"dimensions":[53],"over":[54,77,154],"alphabets.":[56],"The":[57,83],"second":[58],"problem":[59,85],"solve":[61],"is":[62,86],"construction":[63,123],"diametric":[65],"perfect":[66],"with":[68,93,99],"minimum":[69],"distance":[70],"four.":[71],"We":[72],"will":[73,130],"construct":[74],"such":[75],"various":[78],"lengths":[79],"alphabet":[81],"sizes.":[82],"third":[84],"to":[87,148],"transfer":[88],"an":[89,112],"n-dimensional":[90],"sphere":[92,138],"large":[94],"radius":[95],"into":[96],"shape,":[98],"same":[101],"volume,":[102],"located":[103],"box.":[108],"Hadamard":[109,128],"matrices":[110,129],"play":[111],"essential":[113],"role":[114],"solutions":[117],"for":[118,141],"all":[119],"three":[120],"problems.":[121],"A":[122],"based":[126],"start":[131],"our":[132],"discussion.":[133],"These":[134],"approach":[136],"packing":[139],"bound":[140],"very":[142],"high":[143],"rate":[144],"range":[145],"appear":[147],"be":[149],"best":[151],"known":[152],"some":[155],"sets":[156],"parameters.":[158]},"counts_by_year":[{"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":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}