{"id":"https://openalex.org/W4396712536","doi":"https://doi.org/10.1109/tcomm.2024.3397795","title":"On the Distribution of Weights Less Than 2<i>w</i> <sub>min</sub>in Polar Codes","display_name":"On the Distribution of Weights Less Than 2<i>w</i> <sub>min</sub>in Polar Codes","publication_year":2024,"publication_date":"2024-05-07","ids":{"openalex":"https://openalex.org/W4396712536","doi":"https://doi.org/10.1109/tcomm.2024.3397795"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2024.3397795","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2024.3397795","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","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/A5034323222","display_name":"Zicheng Ye","orcid":"https://orcid.org/0009-0005-8160-9698"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zicheng Ye","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, CAS, China","Huawei Technologies Co. Ltd, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, CAS, China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Huawei Technologies Co. Ltd, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100694021","display_name":"Yuan Li","orcid":"https://orcid.org/0000-0001-8712-2470"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Li","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, CAS, China","Huawei Technologies Co. Ltd, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, CAS, China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Huawei Technologies Co. Ltd, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074783994","display_name":"Huazi Zhang","orcid":"https://orcid.org/0000-0001-5443-1314"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huazi Zhang","raw_affiliation_strings":["Huawei Technologies Company Ltd., Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100669839","display_name":"Jun Wang","orcid":"https://orcid.org/0000-0002-7684-0191"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Wang","raw_affiliation_strings":["Huawei Technologies Company Ltd., Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100979503","display_name":"Guiying Yan","orcid":"https://orcid.org/0000-0002-1736-5482"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiying Yan","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, CAS, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, CAS, China","institution_ids":["https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078600050","display_name":"Zhi-Ming Ma","orcid":"https://orcid.org/0000-0001-6453-4368"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiming Ma","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, CAS, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, CAS, China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5034323222"],"corresponding_institution_ids":["https://openalex.org/I2250955327","https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":1.8793,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.85175029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"72","issue":"10","first_page":"5988","last_page":"6000"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9785000085830688,"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"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9785000085830688,"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"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9581000208854675,"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":0.954200029373169,"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/polar","display_name":"Polar","score":0.466220885515213},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4288894534111023},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40952563285827637},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3904915153980255},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.35922300815582275},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.34977996349334717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3269617557525635},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.32508939504623413},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2736828029155731},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12026786804199219}],"concepts":[{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.466220885515213},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4288894534111023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40952563285827637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3904915153980255},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.35922300815582275},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.34977996349334717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3269617557525635},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.32508939504623413},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2736828029155731},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12026786804199219},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcomm.2024.3397795","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2024.3397795","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5647958688","display_name":null,"funder_award_id":"2023YFA1009602","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1972808865","https://openalex.org/W1985834029","https://openalex.org/W2004229705","https://openalex.org/W2009101488","https://openalex.org/W2033234285","https://openalex.org/W2035513039","https://openalex.org/W2038242066","https://openalex.org/W2042993834","https://openalex.org/W2059977232","https://openalex.org/W2106045225","https://openalex.org/W2120399748","https://openalex.org/W2121417875","https://openalex.org/W2128552304","https://openalex.org/W2150498905","https://openalex.org/W2264554231","https://openalex.org/W2514963767","https://openalex.org/W2608866305","https://openalex.org/W2756338438","https://openalex.org/W2963710189","https://openalex.org/W2995572641","https://openalex.org/W3198171271","https://openalex.org/W3198322199","https://openalex.org/W4300877731","https://openalex.org/W4372280060","https://openalex.org/W4386072353","https://openalex.org/W6771326266","https://openalex.org/W6851784677"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2885615566","https://openalex.org/W1973916483","https://openalex.org/W1996076013","https://openalex.org/W2065102984","https://openalex.org/W2025479331","https://openalex.org/W2149101979","https://openalex.org/W3186443608","https://openalex.org/W1502590441","https://openalex.org/W2083362239"],"abstract_inverted_index":{"The":[0],"number":[1,67],"of":[2,10,21,68],"low-weight":[3],"codewords":[4,20,69],"is":[5],"critical":[6],"to":[7,56,97],"the":[8,19,46,62,66,87,98],"performance":[9],"error-correcting":[11],"codes.":[12,59],"In":[13,49],"1970,":[14],"Kasami":[15],"and":[16],"Tokura":[17],"characterized":[18],"Reed-Muller":[22],"(RM)":[23],"codes":[24,73],"whose":[25],"weights":[26,75],"are":[27],"less":[28,76],"than":[29,77],"2":[30,78],"<italic":[31,39,79],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[32,35,40,43,80,83],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">w</i>":[33,41,81],"<sub":[34,42,82],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">min</sub>":[36,44,84],",":[37],"where":[38],"represents":[45],"minimum":[47],"weight.":[48],"this":[50],"paper,":[51],"we":[52],"extend":[53],"their":[54],"results":[55],"decreasing":[57,71],"polar":[58,72],"We":[60],"present":[61],"closed-form":[63],"expressions":[64],"for":[65],"in":[70,92],"with":[74,95],".":[85],"Moreover,":[86],"proposed":[88],"enumeration":[89],"algorithm":[90],"runs":[91],"polynomial":[93],"time":[94],"respect":[96],"code":[99],"length.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}