{"id":"https://openalex.org/W1903621387","doi":"https://doi.org/10.1109/tit.2015.2477822","title":"Optimal Codes With Limited Kraft Sum","display_name":"Optimal Codes With Limited Kraft Sum","publication_year":2015,"publication_date":"2015-09-10","ids":{"openalex":"https://openalex.org/W1903621387","doi":"https://doi.org/10.1109/tit.2015.2477822","mag":"1903621387"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2477822","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2477822","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/A5026035440","display_name":"Adel Aghajan","orcid":"https://orcid.org/0000-0003-0329-6102"},"institutions":[{"id":"https://openalex.org/I170013655","display_name":"Isfahan University of Technology","ror":"https://ror.org/00af3sa43","country_code":"IR","type":"education","lineage":["https://openalex.org/I170013655"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Adel Aghajan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran","Department of Electrical and computer engineering, Isfahan University of Technology, Isfahan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran","institution_ids":["https://openalex.org/I170013655"]},{"raw_affiliation_string":"Department of Electrical and computer engineering, Isfahan University of Technology, Isfahan, Iran","institution_ids":["https://openalex.org/I170013655"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090381199","display_name":"Mohammadali Khosravifard","orcid":"https://orcid.org/0000-0002-0645-7285"},"institutions":[{"id":"https://openalex.org/I170013655","display_name":"Isfahan University of Technology","ror":"https://ror.org/00af3sa43","country_code":"IR","type":"education","lineage":["https://openalex.org/I170013655"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammadali Khosravifard","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran","Department of Electrical and computer engineering, Isfahan University of Technology, Isfahan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran","institution_ids":["https://openalex.org/I170013655"]},{"raw_affiliation_string":"Department of Electrical and computer engineering, Isfahan University of Technology, Isfahan, Iran","institution_ids":["https://openalex.org/I170013655"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170013655"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03161156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"11","first_page":"6385","last_page":"6394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","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/T11269","display_name":"Algorithms and Data Compression","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/T11567","display_name":"semigroups and automata theory","score":0.9973000288009644,"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/T12029","display_name":"DNA and Biological Computing","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5193215608596802},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5121612548828125},{"id":"https://openalex.org/keywords/huffman-coding","display_name":"Huffman coding","score":0.5047591924667358},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44715261459350586},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4439549446105957},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38272571563720703},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3318325877189636},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3096053898334503},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.21111491322517395},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.20894458889961243},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20009645819664001}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5193215608596802},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5121612548828125},{"id":"https://openalex.org/C46900642","wikidata":"https://www.wikidata.org/wiki/Q2647","display_name":"Huffman coding","level":3,"score":0.5047591924667358},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44715261459350586},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4439549446105957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38272571563720703},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3318325877189636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3096053898334503},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.21111491322517395},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.20894458889961243},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20009645819664001},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2015.2477822","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2477822","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":18,"referenced_works":["https://openalex.org/W1578978375","https://openalex.org/W1597182570","https://openalex.org/W1984577633","https://openalex.org/W2018250045","https://openalex.org/W2022421187","https://openalex.org/W2038649859","https://openalex.org/W2043622336","https://openalex.org/W2046171733","https://openalex.org/W2060108852","https://openalex.org/W2072549963","https://openalex.org/W2083368438","https://openalex.org/W2149258547","https://openalex.org/W2159381752","https://openalex.org/W2166451469","https://openalex.org/W2169389509","https://openalex.org/W2478708596","https://openalex.org/W6634800051","https://openalex.org/W6635812967"],"related_works":["https://openalex.org/W2351464472","https://openalex.org/W3163059229","https://openalex.org/W1518463267","https://openalex.org/W2586352442","https://openalex.org/W4287181776","https://openalex.org/W2914103308","https://openalex.org/W2357109835","https://openalex.org/W2363764423","https://openalex.org/W2344988652","https://openalex.org/W3022794168"],"abstract_inverted_index":{"The":[0,144],"well-known":[1],"Huffman":[2,58],"algorithm":[3,109],"is":[4,35,45,69],"an":[5,32],"elegant":[6],"approach":[7],"to":[8,27,47,104,110],"solve":[9],"the":[10,15,38,42,55,62,66,79,83,97,112,132],"basic":[11],"problem":[12,34],"of":[13,41,65,82,91],"finding":[14],"optimal":[16,67,84,113],"code":[17,68,85],"among":[18],"those":[19],"with":[20,115,137],"Kraft":[21,39,63,80,116,140],"sums":[22],"smaller":[23],"than":[24],"or":[25],"equal":[26,72,118],"1.":[28],"In":[29],"this":[30],"paper,":[31],"extended":[33],"investigated,":[36],"where":[37],"sum":[40,64,81,117],"usable":[43],"codes":[44],"limited":[46],"a":[48,88,107,123,138,149],"given":[49],"real":[50],"number$\\gamma":[51],"$,$0&lt;\\gamma":[52],"&lt;1$.":[53,158],"Unlike":[54],"case$\\gamma":[56],"=1$(i.e.,":[57],"coding),":[59],"for$\\gamma":[60,157],"&lt;1$,":[61],"not":[70],"necessarily":[71],"to$\\gamma":[73,119],"$.":[74,100],"However,":[75],"we":[76],"show":[77],"that":[78,155],"lies":[86],"in":[87,152],"finite":[89,124],"set":[90,133],"rational":[92],"numbers":[93],"which":[94],"depend":[95],"on":[96],"value":[98],"of$\\gamma":[99,147],"This":[101],"motivates":[102],"us":[103],"first":[105],"devise":[106],"recursive":[108],"obtain":[111],"codelengths":[114],"'$,":[120],"where$\\gamma":[121],"'$has":[122],"binary":[125,145],"representation":[126,146],"and$0&lt;\\gamma":[127],"'&lt;1$.":[128],"To":[129],"do":[130],"so,":[131],"of$N$-tuple":[134],"codelength":[135],"vectors":[136],"specific":[139],"sum$\\gamma":[141],"'$is":[142],"characterized.":[143],"$plays":[148],"fundamental":[150],"role":[151],"all":[153],"problems":[154],"arise":[156]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
