{"id":"https://openalex.org/W2028042041","doi":"https://doi.org/10.1109/ita.2010.5454120","title":"On weight enumerators and MacWilliams identity for convolutional codes","display_name":"On weight enumerators and MacWilliams identity for convolutional codes","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2028042041","doi":"https://doi.org/10.1109/ita.2010.5454120","mag":"2028042041"},"language":"en","primary_location":{"id":"doi:10.1109/ita.2010.5454120","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ita.2010.5454120","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 Information Theory and Applications Workshop (ITA)","raw_type":"proceedings-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/A5018999589","display_name":"Irina E. Bocharova","orcid":"https://orcid.org/0000-0002-6460-4626"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I173089394","display_name":"ITMO University","ror":"https://ror.org/04txgxn49","country_code":"RU","type":"education","lineage":["https://openalex.org/I173089394"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Irina E. Bocharova","raw_affiliation_strings":["Department of Information Systems, Saint Petersburg University of Information Technologies, Saint Petersburg, Russia","Department of Information Systems, St. Petersburg University of Information Technologies, Mechanics and Optics, St. Petersburg, 197101, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Systems, Saint Petersburg University of Information Technologies, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I173089394"]},{"raw_affiliation_string":"Department of Information Systems, St. Petersburg University of Information Technologies, Mechanics and Optics, St. Petersburg, 197101, Russia","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107233585","display_name":"Florian Hug","orcid":null},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Florian Hug","raw_affiliation_strings":["Department of Electrical and Information Technology, Lund University, Lund, Sweden","Dept. of Electrical and Information Technology, Lund University, P.O. Box 118, SE-22100 Lund, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Information Technology, Lund University, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]},{"raw_affiliation_string":"Dept. of Electrical and Information Technology, Lund University, P.O. Box 118, SE-22100 Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044516030","display_name":"Rolf Johannesson","orcid":null},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Rolf Johannesson","raw_affiliation_strings":["Department of Electrical and Information Technology, Lund University, Lund, Sweden","Dept. of Electrical and Information Technology, Lund University, P.O. Box 118, SE-22100 Lund, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Information Technology, Lund University, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]},{"raw_affiliation_string":"Dept. of Electrical and Information Technology, Lund University, P.O. Box 118, SE-22100 Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088880021","display_name":"Boris D. Kudryashov","orcid":"https://orcid.org/0000-0002-5865-5283"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I173089394","display_name":"ITMO University","ror":"https://ror.org/04txgxn49","country_code":"RU","type":"education","lineage":["https://openalex.org/I173089394"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Boris D. Kudryashov","raw_affiliation_strings":["Department of Information Systems, Saint Petersburg University of Information Technologies, Saint Petersburg, Russia","Department of Information Systems, St. Petersburg University of Information Technologies, Mechanics and Optics, St. Petersburg, 197101, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Systems, Saint Petersburg University of Information Technologies, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I173089394"]},{"raw_affiliation_string":"Department of Information Systems, St. Petersburg University of Information Technologies, Mechanics and Optics, St. Petersburg, 197101, Russia","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8646,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.87396679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","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/T11130","display_name":"Coding theory and cryptography","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/T12162","display_name":"Cellular Automata and Applications","score":0.9991000294685364,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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":0.8045358657836914},{"id":"https://openalex.org/keywords/convolutional-code","display_name":"Convolutional code","score":0.7932592630386353},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5292365550994873},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5237869024276733},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.47697457671165466},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46436187624931335},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.4618377387523651},{"id":"https://openalex.org/keywords/dual-code","display_name":"Dual code","score":0.4544960558414459},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4173544943332672},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38068071007728577},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3546893000602722},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33677634596824646},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.23961162567138672},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17726388573646545},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.17022114992141724},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.059634238481521606}],"concepts":[{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.8045358657836914},{"id":"https://openalex.org/C157899210","wikidata":"https://www.wikidata.org/wiki/Q1395022","display_name":"Convolutional code","level":3,"score":0.7932592630386353},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5292365550994873},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5237869024276733},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.47697457671165466},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46436187624931335},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.4618377387523651},{"id":"https://openalex.org/C73666251","wikidata":"https://www.wikidata.org/wiki/Q5310189","display_name":"Dual code","level":5,"score":0.4544960558414459},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4173544943332672},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38068071007728577},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3546893000602722},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33677634596824646},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.23961162567138672},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17726388573646545},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.17022114992141724},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.059634238481521606},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/ita.2010.5454120","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ita.2010.5454120","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 Information Theory and Applications Workshop (ITA)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.409.1836","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.1836","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ita.ucsd.edu/workshop/10/files/paper/paper_1887.pdf","raw_type":"text"},{"id":"pmh:oai:lup.lub.lu.se:68a6cbe2-b547-4917-81e2-91fc27f94233","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/1539098","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W84524834","https://openalex.org/W1606480398","https://openalex.org/W1814194507","https://openalex.org/W1836967236","https://openalex.org/W1867117520","https://openalex.org/W1996491504","https://openalex.org/W2008392059","https://openalex.org/W2051560422","https://openalex.org/W2085530959","https://openalex.org/W2122683098","https://openalex.org/W2123853131","https://openalex.org/W2143733873","https://openalex.org/W2169362094","https://openalex.org/W2963997115","https://openalex.org/W4242536966","https://openalex.org/W6636396655"],"related_works":["https://openalex.org/W1579051351","https://openalex.org/W2771127828","https://openalex.org/W2099549796","https://openalex.org/W2161282249","https://openalex.org/W1867117520","https://openalex.org/W2052380558","https://openalex.org/W2131338819","https://openalex.org/W2051560422","https://openalex.org/W4237142313","https://openalex.org/W3022893113"],"abstract_inverted_index":{"Convolutional":[0],"codes":[1,41,72,112],"are":[2,16,22,119],"defined":[3,23],"to":[4,24,121],"be":[5,25],"equivalent":[6,27,32],"if":[7,29],"their":[8,74],"code":[9,90,98],"symbols":[10],"differ":[11],"only":[12],"in":[13],"how":[14],"they":[15,30],"ordered":[17],"and":[18,53,73,115],"two":[19],"generator":[20,46],"matrices":[21,47],"weakly":[26],"(WE)":[28],"encode":[31],"convolutional":[33,40,63,71,89,97,111],"codes.":[34,64,127],"It":[35,80],"is":[36,81,91,113],"shown":[37,82],"that":[38,56,83],"tailbiting":[39],"encoded":[42],"by":[43],"WE":[44],"minimal-basic":[45],"have":[48],"the":[49,67,84,107,116,124],"same":[50],"spectra.":[51],"Shearer":[52],"McEliece":[54],"showed":[55],"MacWilliams":[57,76],"identity":[58,77],"does":[59],"not":[60,92],"hold":[61],"for":[62,66,106,123],"However,":[65],"spectra":[68,108],"of":[69,86,95,109],"truncated":[70,88,110],"duals,":[75],"clearly":[78],"holds.":[79],"dual":[85,126],"a":[87,93,96,104],"truncation":[94],"but":[99],"its":[100],"reversal":[101],"is.":[102],"Finally,":[103],"recursion":[105],"given":[114],"spectral":[117],"components":[118],"related":[120],"those":[122],"corresponding":[125]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
