{"id":"https://openalex.org/W1962448616","doi":"https://doi.org/10.1109/tit.2011.2162272","title":"Second-Order Weight Distributions","display_name":"Second-Order Weight Distributions","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W1962448616","doi":"https://doi.org/10.1109/tit.2011.2162272","mag":"1962448616"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2162272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162272","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/1007.3108","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shengtian Yang","raw_affiliation_strings":["Hangzhou, China","Zhengyuan Xiaoqu, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Hangzhou, China","institution_ids":[]},{"raw_affiliation_string":"Zhengyuan Xiaoqu, Hangzhou, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022398344"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7308,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71623355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"57","issue":"9","first_page":"6068","last_page":"6077"},"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/T12029","display_name":"DNA and Biological Computing","score":0.9987999796867371,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.8138717412948608},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.7790581583976746},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7676429748535156},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.6010464429855347},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.5600691437721252},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.47398367524147034},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4731408655643463},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.4643680453300476},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.43352729082107544},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4188990890979767},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41769498586654663},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.2534991502761841},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2446841597557068},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.17293792963027954},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09003058075904846}],"concepts":[{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.8138717412948608},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.7790581583976746},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7676429748535156},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.6010464429855347},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.5600691437721252},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.47398367524147034},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4731408655643463},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.4643680453300476},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.43352729082107544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4188990890979767},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41769498586654663},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2534991502761841},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2446841597557068},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.17293792963027954},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09003058075904846},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2011.2162272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162272","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:1007.3108","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1007.3108","pdf_url":"https://arxiv.org/pdf/1007.3108","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:10.1.1.753.322","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.753.322","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/1007.3108.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1007.3108","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1007.3108","pdf_url":"https://arxiv.org/pdf/1007.3108","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W147465018","https://openalex.org/W947704800","https://openalex.org/W1521367167","https://openalex.org/W1536930200","https://openalex.org/W1551018093","https://openalex.org/W1559343931","https://openalex.org/W1575217484","https://openalex.org/W1579739595","https://openalex.org/W1973174922","https://openalex.org/W1984049650","https://openalex.org/W1989606418","https://openalex.org/W1989754079","https://openalex.org/W1993359877","https://openalex.org/W2026314858","https://openalex.org/W2040009340","https://openalex.org/W2043151582","https://openalex.org/W2064736023","https://openalex.org/W2088587246","https://openalex.org/W2089196531","https://openalex.org/W2095547380","https://openalex.org/W2096667287","https://openalex.org/W2101783382","https://openalex.org/W2102541782","https://openalex.org/W2108489927","https://openalex.org/W2110954483","https://openalex.org/W2115104320","https://openalex.org/W2121200658","https://openalex.org/W2121606987","https://openalex.org/W2126276563","https://openalex.org/W2128552304","https://openalex.org/W2128765501","https://openalex.org/W2134959754","https://openalex.org/W2137308661","https://openalex.org/W2137699000","https://openalex.org/W2145789487","https://openalex.org/W2146774798","https://openalex.org/W2158309140","https://openalex.org/W2163228498","https://openalex.org/W2163496715","https://openalex.org/W2169732368","https://openalex.org/W2987657883","https://openalex.org/W3099582772","https://openalex.org/W3104692007","https://openalex.org/W3105487673","https://openalex.org/W3105490918","https://openalex.org/W4206373597","https://openalex.org/W4206738103","https://openalex.org/W4206775542","https://openalex.org/W4233910079","https://openalex.org/W4234572373","https://openalex.org/W4248604894","https://openalex.org/W4300188436"],"related_works":["https://openalex.org/W4247927056","https://openalex.org/W2131338819","https://openalex.org/W3172978644","https://openalex.org/W4237142313","https://openalex.org/W1962448616","https://openalex.org/W2963553930","https://openalex.org/W2389453929","https://openalex.org/W1579051351","https://openalex.org/W4304127749","https://openalex.org/W4206974355"],"abstract_inverted_index":{"A":[0,27],"fundamental":[1,165],"property":[2,153],"of":[3,20,23,29,47,56,70,73,83,97,120,122,145,178],"codes,":[4],"the":[5,13,67,81,98,123,151,157],"second-order":[6,40,53,84,94,158],"weight":[7,21,35,41,54,71,85,95,159],"distribution,":[8,160],"is":[9,37,50,91,117,133,148,154,182],"proposed":[10],"to":[11,32,185],"solve":[12],"problems":[14,138,170],"such":[15],"as":[16],"computing":[17],"second":[18,68],"moments":[19,69],"distributions":[22,55,72,86,96],"linear":[24,179],"code":[25,59,76],"ensembles.":[26],"series":[28],"results,":[30],"parallel":[31],"those":[33],"for":[34,39,136],"distributions,":[36],"established":[38],"distributions.":[42],"In":[43],"particular,":[44],"an":[45],"analogue":[46],"MacWilliams":[48],"identities":[49],"proved.":[51],"The":[52,93],"regular":[57,74],"LDPC":[58,75],"ensembles":[60,77,99],"are":[61,78,110],"then":[62],"computed.":[63],"As":[64],"easy":[65],"consequences,":[66],"obtained.":[79],"Furthermore,":[80],"application":[82],"in":[87,156,167,171],"random":[88,105,115,126],"coding":[89,172],"approach":[90],"discussed.":[92],"generated":[100],"by":[101],"a":[102,113,118,129,164],"so-called":[103],"2-good":[104,114,152],"generator":[106],"or":[107,142],"parity-check":[108],"matrix":[109,116,127],"computed,":[111],"where":[112],"kind":[119],"generalization":[121],"uniformly":[124],"distributed":[125],"over":[128],"finite":[130],"filed":[131],"and":[132,174],"very":[134],"useful":[135],"solving":[137],"that":[139,150],"involve":[140],"pairwise":[141],"triple-wise":[143],"properties":[144],"sequences.":[146],"It":[147],"shown":[149],"reflected":[155],"which":[161],"thus":[162],"plays":[163],"role":[166],"some":[168],"well-known":[169],"theory":[173],"combinatorics.":[175],"An":[176],"example":[177],"intersecting":[180],"codes":[181],"finally":[183],"provided":[184],"illustrate":[186],"this":[187],"fact.":[188]},"counts_by_year":[{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
