{"id":"https://openalex.org/W2022252420","doi":"https://doi.org/10.1109/tit.1980.1056199","title":"Combinatorial properties of good codes for binary autoregressive sources (Corresp.)","display_name":"Combinatorial properties of good codes for binary autoregressive sources (Corresp.)","publication_year":1980,"publication_date":"1980-05-01","ids":{"openalex":"https://openalex.org/W2022252420","doi":"https://doi.org/10.1109/tit.1980.1056199","mag":"2022252420"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1980.1056199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056199","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/A5109153224","display_name":"P. Delsarte","orcid":null},"institutions":[{"id":"https://openalex.org/I4210159858","display_name":"Philips (Belgium)","ror":"https://ror.org/05bsjqt55","country_code":"BE","type":"company","lineage":["https://openalex.org/I4210122849","https://openalex.org/I4210159858"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"P. Delsarte","raw_affiliation_strings":["Philips Research National Laboratory, Brussels, Belgium"],"affiliations":[{"raw_affiliation_string":"Philips Research National Laboratory, Brussels, Belgium","institution_ids":["https://openalex.org/I4210159858"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111796032","display_name":"P. Piret","orcid":null},"institutions":[{"id":"https://openalex.org/I4210159858","display_name":"Philips (Belgium)","ror":"https://ror.org/05bsjqt55","country_code":"BE","type":"company","lineage":["https://openalex.org/I4210122849","https://openalex.org/I4210159858"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P. Piret","raw_affiliation_strings":["Philips Research National Laboratory, Brussels, Belgium"],"affiliations":[{"raw_affiliation_string":"Philips Research National Laboratory, Brussels, Belgium","institution_ids":["https://openalex.org/I4210159858"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109153224"],"corresponding_institution_ids":["https://openalex.org/I4210159858"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16911267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"3","first_page":"341","last_page":"345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998000264167786,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9994999766349792,"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":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5792089104652405},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5711860060691833},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4811769425868988},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.46069806814193726},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37538599967956543},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34807318449020386},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32836097478866577},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27709728479385376},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09871917963027954},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.07094421982765198}],"concepts":[{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5792089104652405},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5711860060691833},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4811769425868988},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.46069806814193726},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37538599967956543},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34807318449020386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32836097478866577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27709728479385376},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09871917963027954},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.07094421982765198},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1980.1056199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056199","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1498084283","https://openalex.org/W1989008275","https://openalex.org/W1990992471","https://openalex.org/W2110478863","https://openalex.org/W2118312589","https://openalex.org/W2122116319","https://openalex.org/W2153815969","https://openalex.org/W2182112064","https://openalex.org/W3151409487","https://openalex.org/W4301441647","https://openalex.org/W6629514076"],"related_works":["https://openalex.org/W2943247777","https://openalex.org/W2740543340","https://openalex.org/W2371167013","https://openalex.org/W1493958394","https://openalex.org/W1582340598","https://openalex.org/W2794545997","https://openalex.org/W2584980534","https://openalex.org/W2182731056","https://openalex.org/W1600949677","https://openalex.org/W2779867339"],"abstract_inverted_index":{"Let":[0],"<tex":[1,17,23,29,38,47,58,84,128,140,146,155,161,171,180,190],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,18,24,30,39,48,59,85,129,141,147,156,162,172,181,191],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">M</tex>":[3,60],"be":[4,10,134],"a":[5,13,100],"binary":[6,22],"autoregressive":[7],"source":[8,57],"to":[9,133,179],"encoded":[11],"within":[12],"specified":[14],"Hamming":[15,111],"distortion":[16],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\delta</tex>":[19],".":[20,61,193],"A":[21],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</tex>":[25,142,157],"-tuple":[26],"is":[27,35,63,75,93,98,103,109,119,131,168],"called":[28],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\sigma</tex>":[31,86],"-central":[32,87],"if":[33,127],"it":[34,167],"at":[36,45,144],"distance":[37,145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\leq":[40,148],"n(\\delta":[41],"+":[42],"\\sigma)</tex>":[43],"from":[44,153],"least":[46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2^{nH(\\delta":[49],"-":[50],"\\sigma)}</tex>":[51],"typical":[52,139],"sequences":[53],"produced":[54],"by":[55,105],"the":[56,68,71,90,95,110,122,135,154],"It":[62],"first":[64],"shown":[65,169],"that,":[66],"in":[67],"region":[69],"where":[70],"Shannon":[72],"rate-distortion":[73],"bound":[74],"achieved,":[76],"there":[77],"exist":[78],"\"good":[79],"codes\"":[80],"consisting":[81],"only":[82],"of":[83,113,138,159,189],"words.":[88],"Next,":[89],"characterization":[91],"problem":[92,118],"studied;":[94],"basic":[96],"conjecture":[97],"that":[99,170],"central":[101],"sequence":[102],"well-characterized":[104],"its":[106],"level,":[107],"which":[108],"weight":[112],"an":[114,184],"image":[115],"sequence.":[116],"The":[117],"solved":[120],"for":[121,183],"memoryless":[123],"source.":[124],"In":[125],"general,":[126],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N(k,r)</tex>":[130],"defined":[132],"mean":[136],"number":[137],"-tuples":[143,158],"r":[149],"=":[150],"n":[151],"\\delta</tex>":[152],"level":[160],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k=n":[163],"\\xi</tex>":[164],",":[165],"then":[166],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n^{-l}":[173],"\\log":[174],"N(k,r)</tex>":[175],"becomes":[176],"arbitrarily":[177],"close":[178],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">H(\\delta)</tex>":[182],"explicitly":[185],"determined":[186],"unique":[187],"value":[188],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\xi</tex>":[192]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}