{"id":"https://openalex.org/W2089606264","doi":"https://doi.org/10.1137/s0895480198350057","title":"Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences","display_name":"Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2089606264","doi":"https://doi.org/10.1137/s0895480198350057","mag":"2089606264"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480198350057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480198350057","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5050062480","display_name":"Anne Canteaut","orcid":"https://orcid.org/0000-0002-6292-8336"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Anne Canteaut","raw_affiliation_strings":["INRIA, projet CODES, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, projet CODES, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048217797","display_name":"Pascale Charpin","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pascale Charpin","raw_affiliation_strings":["INRIA, projet CODES, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, projet CODES, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107119162","display_name":"Hans Dobbertin","orcid":null},"institutions":[{"id":"https://openalex.org/I1317578790","display_name":"Federal Office for Information Security","ror":"https://ror.org/03v7mmm26","country_code":"DE","type":"other","lineage":["https://openalex.org/I1317578790"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans Dobbertin","raw_affiliation_strings":["German Information Security Agency, P.O. Box 20 03 63, D-53133 Bonn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"German Information Security Agency, P.O. Box 20 03 63, D-53133 Bonn, Germany","institution_ids":["https://openalex.org/I1317578790"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8407,"has_fulltext":false,"cited_by_count":145,"citation_normalized_percentile":{"value":0.96047839,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"13","issue":"1","first_page":"105","last_page":"138"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9976000189781189,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.98580002784729,"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":0.8916487097740173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8821182250976562},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.6535975337028503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6300684809684753},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5166014432907104},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4649347960948944},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.14822432398796082}],"concepts":[{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.8916487097740173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8821182250976562},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.6535975337028503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6300684809684753},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5166014432907104},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4649347960948944},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.14822432398796082}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895480198350057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480198350057","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.6663","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.6663","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-rocq.inria.fr/codes/Anne.Canteaut/Publications/Canteaut_Charpin_Dobbertin00b.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1528065150","https://openalex.org/W1531334709","https://openalex.org/W1537206908","https://openalex.org/W1554932142","https://openalex.org/W1575149347","https://openalex.org/W1587687098","https://openalex.org/W1629301835","https://openalex.org/W1964723977","https://openalex.org/W1972817581","https://openalex.org/W1978695162","https://openalex.org/W1980099675","https://openalex.org/W1983818679","https://openalex.org/W2003156157","https://openalex.org/W2015894712","https://openalex.org/W2021706119","https://openalex.org/W2024483577","https://openalex.org/W2024729203","https://openalex.org/W2040354470","https://openalex.org/W2043200151","https://openalex.org/W2048462185","https://openalex.org/W2067096554","https://openalex.org/W2087896741","https://openalex.org/W2089277105","https://openalex.org/W2105476675","https://openalex.org/W2131820257","https://openalex.org/W2135168820","https://openalex.org/W2137326899","https://openalex.org/W2138238405","https://openalex.org/W2167433347","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2014175480","https://openalex.org/W1036096233","https://openalex.org/W64298394","https://openalex.org/W4367549511","https://openalex.org/W2035991160","https://openalex.org/W2907189760","https://openalex.org/W2982361184","https://openalex.org/W2009615080","https://openalex.org/W2041496871","https://openalex.org/W2035506078"],"abstract_inverted_index":{"We":[0,46],"study":[1],"[2m-1,2m]-binary":[2],"linear":[3],"codes":[4,21,53,82],"whose":[5,25],"weights":[6],"lie":[7],"between":[8],"w0":[9,13],"and":[10,37,61],"2m-w0,":[11],"where":[12],"takes":[14],"the":[15,75],"highest":[16],"possible":[17],"value.":[18],"Primitive":[19],"cyclic":[20,81],"with":[22,43,83],"two":[23,84],"zeros":[24],"dual":[26,59],"satisfies":[27],"this":[28],"property":[29],"actually":[30],"correspond":[31],"to":[32,38],"almost":[33],"bent":[34],"power":[35],"functions":[36],"pairs":[39,93],"of":[40,78,80,92,94],"maximum-length":[41,95],"sequences":[42,96],"preferred":[44],"crosscorrelation.":[45],"prove":[47],"that,":[48],"for":[49],"odd":[50],"m,":[51],"these":[52],"are":[54,98],"completely":[55],"characterized":[56],"by":[57,62],"their":[58,63],"distance":[60],"weight":[64,76],"divisibility.":[65],"Using":[66],"McEliece's":[67],"theorem":[68],"we":[69,87],"give":[70],"some":[71,89],"general":[72],"results":[73],"on":[74],"divisibility":[77],"duals":[79],"zeros;":[85],"specifically,":[86],"exhibit":[88],"infinite":[90],"families":[91],"which":[97],"not":[99],"preferred.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":10}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
