{"id":"https://openalex.org/W4229021507","doi":"https://doi.org/10.1007/s10623-022-01047-x","title":"On permutation quadrinomials with boomerang uniformity 4 and the best-known nonlinearity","display_name":"On permutation quadrinomials with boomerang uniformity 4 and the best-known nonlinearity","publication_year":2022,"publication_date":"2022-05-07","ids":{"openalex":"https://openalex.org/W4229021507","doi":"https://doi.org/10.1007/s10623-022-01047-x"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-022-01047-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-022-01047-x","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","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/A5100708407","display_name":"Kwang Ho Kim","orcid":"https://orcid.org/0000-0001-7401-717X"},"institutions":[{"id":"https://openalex.org/I3131980609","display_name":"Korean Academy of Science and Technology","ror":"https://ror.org/01j49yd81","country_code":"KR","type":"education","lineage":["https://openalex.org/I3131980609"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Kwang Ho Kim","raw_affiliation_strings":["Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People\u2019s Republic of Korea","PGItech Corp., Pyongyang, Democratic People\u2019s Republic of Korea","Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People's Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People\u2019s Republic of Korea","institution_ids":["https://openalex.org/I3131980609"]},{"raw_affiliation_string":"PGItech Corp., Pyongyang, Democratic People\u2019s Republic of Korea","institution_ids":[]},{"raw_affiliation_string":"Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People's Republic of Korea","institution_ids":["https://openalex.org/I3131980609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034752358","display_name":"Sihem Mesnager","orcid":"https://orcid.org/0000-0003-4008-2031"},"institutions":[{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I48825208","display_name":"Universit\u00e9 Paris 8","ror":"https://ror.org/04wez5e68","country_code":"FR","type":"education","lineage":["https://openalex.org/I48825208"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Sihem Mesnager","raw_affiliation_strings":["Department of Mathematics, University of Paris VIII, 93526, Saint-Denis, France","Telecom Paris, Polytechnic Institute of Paris, 91120, Palaiseau, France","University Sorbonne Paris Cit\u00e9, LAGA, UMR 7539, CNRS, 93430, Villetaneuse, France"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Paris VIII, 93526, Saint-Denis, France","institution_ids":["https://openalex.org/I48825208"]},{"raw_affiliation_string":"Telecom Paris, Polytechnic Institute of Paris, 91120, Palaiseau, France","institution_ids":["https://openalex.org/I12356871"]},{"raw_affiliation_string":"University Sorbonne Paris Cit\u00e9, LAGA, UMR 7539, CNRS, 93430, Villetaneuse, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210102686","https://openalex.org/I4210091437","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044885010","display_name":"Jong Hyok Choe","orcid":null},"institutions":[{"id":"https://openalex.org/I3131980609","display_name":"Korean Academy of Science and Technology","ror":"https://ror.org/01j49yd81","country_code":"KR","type":"education","lineage":["https://openalex.org/I3131980609"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jong Hyok Choe","raw_affiliation_strings":["Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People\u2019s Republic of Korea","Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People's Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People\u2019s Republic of Korea","institution_ids":["https://openalex.org/I3131980609"]},{"raw_affiliation_string":"Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People's Republic of Korea","institution_ids":["https://openalex.org/I3131980609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017311784","display_name":"Dok Nam Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I3131980609","display_name":"Korean Academy of Science and Technology","ror":"https://ror.org/01j49yd81","country_code":"KR","type":"education","lineage":["https://openalex.org/I3131980609"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Dok Nam Lee","raw_affiliation_strings":["Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People\u2019s Republic of Korea","Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People's Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People\u2019s Republic of Korea","institution_ids":["https://openalex.org/I3131980609"]},{"raw_affiliation_string":"Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People's Republic of Korea","institution_ids":["https://openalex.org/I3131980609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017320226","display_name":"Sengsan Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sengsan Lee","raw_affiliation_strings":["Pyongyang University of Computer Science, Pyongyang, Democratic People\u2019s Republic of Korea","Pyongyang University of Computer Science, Pyongyang, Democratic People's Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Pyongyang University of Computer Science, Pyongyang, Democratic People\u2019s Republic of Korea","institution_ids":[]},{"raw_affiliation_string":"Pyongyang University of Computer Science, Pyongyang, Democratic People's Republic of Korea","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040785522","display_name":"Myong Chol Jo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Myong Chol Jo","raw_affiliation_strings":["PGItech Corp., Pyongyang, Democratic People\u2019s Republic of Korea","PGItech Corp., Pyongyang, Democratic People's Republic of Korea"],"affiliations":[{"raw_affiliation_string":"PGItech Corp., Pyongyang, Democratic People\u2019s Republic of Korea","institution_ids":[]},{"raw_affiliation_string":"PGItech Corp., Pyongyang, Democratic People's Republic of Korea","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5034752358"],"corresponding_institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210102686","https://openalex.org/I48825208"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.6551,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.86054701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"90","issue":"6","first_page":"1437","last_page":"1461"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9951000213623047,"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":0.9927999973297119,"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/conjecture","display_name":"Conjecture","score":0.7563368082046509},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6907817721366882},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6839344501495361},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.673879861831665},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6292147636413574},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6061100959777832},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5204037427902222},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.45916682481765747},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3256600499153137},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2545355558395386},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15382763743400574},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1399507224559784}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7563368082046509},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6907817721366882},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6839344501495361},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.673879861831665},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6292147636413574},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6061100959777832},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5204037427902222},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45916682481765747},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3256600499153137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2545355558395386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15382763743400574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1399507224559784},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10623-022-01047-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-022-01047-x","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03960666v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03960666","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, Codes and Cryptography, 2022, 90 (6), pp.1437-1461. &#x27E8;10.1007/s10623-022-01047-x&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W52191336","https://openalex.org/W89216509","https://openalex.org/W1528065150","https://openalex.org/W1553319661","https://openalex.org/W1629301835","https://openalex.org/W1776788878","https://openalex.org/W1971990650","https://openalex.org/W1990773884","https://openalex.org/W2008116785","https://openalex.org/W2022609823","https://openalex.org/W2024385954","https://openalex.org/W2024483577","https://openalex.org/W2041328554","https://openalex.org/W2047794774","https://openalex.org/W2048462185","https://openalex.org/W2048921385","https://openalex.org/W2064186082","https://openalex.org/W2116371502","https://openalex.org/W2294013617","https://openalex.org/W2503574445","https://openalex.org/W2594778474","https://openalex.org/W2778740747","https://openalex.org/W2900658357","https://openalex.org/W2913193769","https://openalex.org/W2931163740","https://openalex.org/W2941076300","https://openalex.org/W2948126476","https://openalex.org/W2963907109","https://openalex.org/W2964299168","https://openalex.org/W3003703995","https://openalex.org/W3003939419","https://openalex.org/W3006479103","https://openalex.org/W3026514873","https://openalex.org/W3035982279","https://openalex.org/W3093954335","https://openalex.org/W3128334180","https://openalex.org/W3135491003","https://openalex.org/W3188039506","https://openalex.org/W4206072275","https://openalex.org/W6601891990"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3162204513","https://openalex.org/W4300899577","https://openalex.org/W2371138613","https://openalex.org/W3194471551","https://openalex.org/W2048963458","https://openalex.org/W4302778552","https://openalex.org/W4247734921","https://openalex.org/W2412284786","https://openalex.org/W2964302506"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
