{"id":"https://openalex.org/W2110954483","doi":"https://doi.org/10.1109/tit.2011.2162642","title":"Weight Distributions of Regular Low-Density Parity-Check Codes Over Finite Fields","display_name":"Weight Distributions of Regular Low-Density Parity-Check Codes Over Finite Fields","publication_year":2011,"publication_date":"2011-08-03","ids":{"openalex":"https://openalex.org/W2110954483","doi":"https://doi.org/10.1109/tit.2011.2162642","mag":"2110954483"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2162642","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162642","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1010.2030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022398344","display_name":"Shengtian Yang","orcid":"https://orcid.org/0000-0003-0255-0471"},"institutions":[{"id":"https://openalex.org/I862669128","display_name":"Xiaomi (China)","ror":"https://ror.org/029f7bn57","country_code":"CN","type":"company","lineage":["https://openalex.org/I862669128"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shengtian Yang","raw_affiliation_strings":["Zhengyuan Xiaoqu, Hangzhou, China","Zhengyuan Xiaoqu 10-2-101, Hangzhou, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Zhengyuan Xiaoqu, Hangzhou, China","institution_ids":[]},{"raw_affiliation_string":"Zhengyuan Xiaoqu 10-2-101, Hangzhou, China#TAB#","institution_ids":["https://openalex.org/I862669128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086666884","display_name":"Thomas Honold","orcid":null},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Thomas Honold","raw_affiliation_strings":["Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","[Dept. of Inf. Sci. & Electron. Eng., Zhejiang Univ., Hangzhou, China]"],"affiliations":[{"raw_affiliation_string":"Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"[Dept. of Inf. Sci. & Electron. Eng., Zhejiang Univ., Hangzhou, China]","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100378052","display_name":"Yan Chen","orcid":"https://orcid.org/0000-0002-0142-4046"},"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":"Yan Chen","raw_affiliation_strings":["Huawei Technologies Company Limited, Shanghai, China","Huawei Technol. Co., Ltd., Shanghai, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Limited, Shanghai, China","institution_ids":["https://openalex.org/I2250955327"]},{"raw_affiliation_string":"Huawei Technol. Co., Ltd., Shanghai, China#TAB#","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100751311","display_name":"Zhaoyang Zhang","orcid":"https://orcid.org/0000-0003-2346-6228"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaoyang Zhang","raw_affiliation_strings":["Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","[Dept. of Inf. Sci. & Electron. Eng., Zhejiang Univ., Hangzhou, China]"],"affiliations":[{"raw_affiliation_string":"Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"[Dept. of Inf. Sci. & Electron. Eng., Zhejiang Univ., Hangzhou, China]","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003311201","display_name":"Peiliang Qiu","orcid":null},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peiliang Qiu","raw_affiliation_strings":["Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","[Dept. of Inf. Sci. & Electron. Eng., Zhejiang Univ., Hangzhou, China]"],"affiliations":[{"raw_affiliation_string":"Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"[Dept. of Inf. Sci. & Electron. Eng., Zhejiang Univ., Hangzhou, China]","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5022398344"],"corresponding_institution_ids":["https://openalex.org/I862669128"],"apc_list":null,"apc_paid":null,"fwci":2.1862,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.88440643,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"57","issue":"11","first_page":"7507","last_page":"7521"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9969000220298767,"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":0.993399977684021,"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/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.9044821262359619},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8190659284591675},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.8090207576751709},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.5560092926025391},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5255024433135986},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.45170652866363525},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3371121287345886},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23677757382392883},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.116341233253479},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08810639381408691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07039815187454224},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.04584631323814392}],"concepts":[{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.9044821262359619},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8190659284591675},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.8090207576751709},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.5560092926025391},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5255024433135986},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.45170652866363525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3371121287345886},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23677757382392883},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.116341233253479},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08810639381408691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07039815187454224},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.04584631323814392},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2011.2162642","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162642","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"},{"id":"pmh:oai:arXiv.org:1010.2030","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1010.2030","pdf_url":"https://arxiv.org/pdf/1010.2030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.750.3434","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.750.3434","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1010.2030.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1010.2030","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1010.2030","pdf_url":"https://arxiv.org/pdf/1010.2030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1559343931","https://openalex.org/W1977104149","https://openalex.org/W2006215437","https://openalex.org/W2043151582","https://openalex.org/W2095151399","https://openalex.org/W2099631789","https://openalex.org/W2102541782","https://openalex.org/W2108489927","https://openalex.org/W2115104320","https://openalex.org/W2117104325","https://openalex.org/W2126276563","https://openalex.org/W2128552304","https://openalex.org/W2128765501","https://openalex.org/W2137699000","https://openalex.org/W2146774798","https://openalex.org/W2163228498","https://openalex.org/W2163496715","https://openalex.org/W2169732368","https://openalex.org/W3104692007","https://openalex.org/W3105490918","https://openalex.org/W4206775542","https://openalex.org/W4242529659","https://openalex.org/W4300188436"],"related_works":["https://openalex.org/W2110954483","https://openalex.org/W2021610081","https://openalex.org/W1976450468","https://openalex.org/W2137543065","https://openalex.org/W2042319752","https://openalex.org/W1988711854","https://openalex.org/W2890903969","https://openalex.org/W2127226704","https://openalex.org/W2963484356","https://openalex.org/W2006215437"],"abstract_inverted_index":{"The":[0],"average":[1,27,50],"weight":[2,28,51],"distribution":[3,29,52],"of":[4,25,39,43,48,75],"a":[5,13,21,37,59,79],"regular":[6,80],"low-density":[7],"parity-check":[8],"(LDPC)":[9],"code":[10,82],"ensemble":[11],"over":[12],"finite":[14],"field":[15],"is":[16,30,69],"thoroughly":[17],"analyzed.":[18],"In":[19],"particular,":[20],"precise":[22],"asymptotic":[23,45],"approximation":[24],"the":[26,33,44,49,72],"derived":[31],"for":[32,71],"small-weight":[34],"case,":[35],"and":[36],"series":[38],"fundamental":[40],"qualitative":[41],"properties":[42],"growth":[46],"rate":[47],"are":[53],"proved.":[54],"Based":[55],"on":[56],"this":[57],"analysis,":[58],"general":[60],"result,":[61],"including":[62],"all":[63],"previous":[64],"results":[65],"as":[66],"special":[67],"cases,":[68],"established":[70],"minimum":[73],"distance":[74],"individual":[76],"codes":[77],"in":[78],"LDPC":[81],"ensemble.":[83]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}