{"id":"https://openalex.org/W2077886255","doi":"https://doi.org/10.1109/tit.2008.2006434","title":"Sharp $p$-Divisibility of Weights in Abelian Codes Over ${\\BBZ}/p^d{\\BBZ}$","display_name":"Sharp $p$-Divisibility of Weights in Abelian Codes Over ${\\BBZ}/p^d{\\BBZ}$","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2077886255","doi":"https://doi.org/10.1109/tit.2008.2006434","mag":"2077886255"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2008.2006434","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2008.2006434","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/A5025565629","display_name":"Daniel Katz","orcid":"https://orcid.org/0000-0003-4600-2629"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel J. Katz","raw_affiliation_strings":["Department of Mathematics, Princeton University, Princeton, NJ, USA","Dept. of Math., Princeton Univ., Princeton, NJ"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Dept. of Math., Princeton Univ., Princeton, NJ","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025565629"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":1.1441,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.8402404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"54","issue":"12","first_page":"5354","last_page":"5380"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9973000288009644,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9965000152587891,"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/divisibility-rule","display_name":"Divisibility rule","score":0.7115035057067871},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5932362675666809},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5232652425765991},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41893717646598816},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.41112610697746277},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37228500843048096},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3659079670906067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29839372634887695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26920661330223083}],"concepts":[{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.7115035057067871},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5932362675666809},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5232652425765991},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41893717646598816},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.41112610697746277},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37228500843048096},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3659079670906067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29839372634887695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26920661330223083},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2008.2006434","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2008.2006434","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":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W179118435","https://openalex.org/W203815528","https://openalex.org/W1494207154","https://openalex.org/W1537327665","https://openalex.org/W1583499453","https://openalex.org/W1627303988","https://openalex.org/W1778220240","https://openalex.org/W1980099675","https://openalex.org/W1983864333","https://openalex.org/W1984121753","https://openalex.org/W1998416663","https://openalex.org/W2010179504","https://openalex.org/W2027216737","https://openalex.org/W2038681062","https://openalex.org/W2043200151","https://openalex.org/W2046280773","https://openalex.org/W2048462185","https://openalex.org/W2058352686","https://openalex.org/W2065264478","https://openalex.org/W2067365716","https://openalex.org/W2069531757","https://openalex.org/W2087074188","https://openalex.org/W2089277105","https://openalex.org/W2089606264","https://openalex.org/W2089777047","https://openalex.org/W2105996438","https://openalex.org/W2107744299","https://openalex.org/W2114808413","https://openalex.org/W2127352809","https://openalex.org/W2129953187","https://openalex.org/W2131820257","https://openalex.org/W2150213879","https://openalex.org/W2161553934","https://openalex.org/W2162118201","https://openalex.org/W2322064007","https://openalex.org/W2601345000","https://openalex.org/W4213348197","https://openalex.org/W4239679971","https://openalex.org/W4247556508","https://openalex.org/W4285719527","https://openalex.org/W6607323702","https://openalex.org/W6735582636"],"related_works":["https://openalex.org/W2943247777","https://openalex.org/W2740543340","https://openalex.org/W2371167013","https://openalex.org/W1582340598","https://openalex.org/W1541021634","https://openalex.org/W2779867339","https://openalex.org/W2794545997","https://openalex.org/W2584980534","https://openalex.org/W2182731056","https://openalex.org/W66917582"],"abstract_inverted_index":{"A":[0],"theorem":[1],"of":[2,10,40,61,76,98,103,131],"McEliece":[3],"on":[4,93,126],"the":[5,58,62,77],"<i":[6,28,63,94,114,127,141],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,19,29,32,64,95,115,118,128,142],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</i>":[8,65,96],"-divisibility":[9,66],"Hamming":[11,99],"weights":[12,100,135],"in":[13,52,68],"cyclic":[14],"codes":[15,25,138],"over":[16,26,112,139],"F":[17],"<sub":[18],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[20],"is":[21],"generalized":[22],"to":[23],"Abelian":[24,110,137],"Zopf":[27,113,140],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">/p</i>":[30,116],"<sup":[31,117],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</sup>":[33,119],"Zopf.":[34,120,144],"This":[35,88],"work":[36],"improves":[37],"upon":[38],"results":[39,92,125],"Helleseth-Kumar-Moreno-Shanbhag,":[41],"Calderbank-Li-Poonen,":[42],"Wilson,":[43],"and":[44,101,133],"Katz.":[45],"These":[46],"previous":[47],"attempts":[48],"are":[49],"not":[50,56],"sharp":[51,91,124],"general,":[53],"i.e.,":[54],"do":[55,72,83],"report":[57],"full":[59],"extent":[60],"except":[67],"special":[69],"cases,":[70],"nor":[71],"they":[73,82],"give":[74],"accounts":[75],"precise":[78],"circumstances":[79],"under":[80],"which":[81],"provide":[84],"best":[85],"possible":[86],"results.":[87],"paper":[89],"provides":[90],"-divisibilities":[97,130],"counts":[102],"any":[104],"particular":[105],"symbol":[106],"for":[107,136],"an":[108],"arbitrary":[109],"code":[111],"It":[121],"also":[122],"presents":[123],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</i>":[129],"Lee":[132],"Euclidean":[134],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">/4</i>":[143]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
