{"id":"https://openalex.org/W4403606921","doi":"https://doi.org/10.1007/s00200-024-00670-6","title":"A degree bound for the c-boomerang uniformity of permutation monomials","display_name":"A degree bound for the c-boomerang uniformity of permutation monomials","publication_year":2024,"publication_date":"2024-10-21","ids":{"openalex":"https://openalex.org/W4403606921","doi":"https://doi.org/10.1007/s00200-024-00670-6"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-024-00670-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-024-00670-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-024-00670-6.pdf","source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00200-024-00670-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001457607","display_name":"Matthias Johann Steiner","orcid":"https://orcid.org/0000-0001-5206-6579"},"institutions":[{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Matthias Johann Steiner","raw_affiliation_strings":["Alpen-Adria-Universit\u00e4t Klagenfurt, Universit\u00e4tsstra\u00dfe 65-67, 9020, Klagenfurt am W\u00f6rthersee, Austria"],"raw_orcid":"https://orcid.org/0000-0001-5206-6579","affiliations":[{"raw_affiliation_string":"Alpen-Adria-Universit\u00e4t Klagenfurt, Universit\u00e4tsstra\u00dfe 65-67, 9020, Klagenfurt am W\u00f6rthersee, Austria","institution_ids":["https://openalex.org/I4210166741"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001457607"],"corresponding_institution_ids":["https://openalex.org/I4210166741"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13219694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"1","first_page":"95","last_page":"130"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9977999925613403,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.8921677470207214},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8684735894203186},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.8246732950210571},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6197488903999329},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5986593961715698},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5530871152877808},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4299442172050476},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37229791283607483},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1733890175819397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06727665662765503}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8921677470207214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8684735894203186},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.8246732950210571},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6197488903999329},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5986593961715698},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5530871152877808},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4299442172050476},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37229791283607483},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1733890175819397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06727665662765503},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00200-024-00670-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-024-00670-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-024-00670-6.pdf","source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00200-024-00670-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-024-00670-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-024-00670-6.pdf","source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2538134746","display_name":"Twinning towards excellence for Privacy Enhancing Technologies leveraging Homomorphic Encryption","funder_award_id":"101079319","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8021791329","display_name":null,"funder_award_id":"725042","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320325472","display_name":"Alpen-Adria-Universit\u00e4t Klagenfurt","ror":"https://ror.org/05q9m0937"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403606921.pdf","grobid_xml":"https://content.openalex.org/works/W4403606921.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W52191336","https://openalex.org/W152855826","https://openalex.org/W632399495","https://openalex.org/W1493026726","https://openalex.org/W1528065150","https://openalex.org/W1550150171","https://openalex.org/W1563341929","https://openalex.org/W1597699498","https://openalex.org/W1965570021","https://openalex.org/W2145038746","https://openalex.org/W2552640487","https://openalex.org/W2732251371","https://openalex.org/W2795355075","https://openalex.org/W2947157832","https://openalex.org/W2977846258","https://openalex.org/W3004692333","https://openalex.org/W3021510930","https://openalex.org/W3035982279","https://openalex.org/W3091014139","https://openalex.org/W3133710726","https://openalex.org/W3140683047","https://openalex.org/W3162268072","https://openalex.org/W3186058725","https://openalex.org/W3193178764","https://openalex.org/W3195145781","https://openalex.org/W3198734649","https://openalex.org/W3201553570","https://openalex.org/W4200466424","https://openalex.org/W4240744875","https://openalex.org/W4240837394","https://openalex.org/W4241072010","https://openalex.org/W4252614677","https://openalex.org/W4298289021","https://openalex.org/W4308361277","https://openalex.org/W4323320096","https://openalex.org/W4365807722","https://openalex.org/W4365808111","https://openalex.org/W4384010359","https://openalex.org/W4385654519","https://openalex.org/W4385654699","https://openalex.org/W4388554180","https://openalex.org/W4396509855","https://openalex.org/W4399554512"],"related_works":["https://openalex.org/W2399505800","https://openalex.org/W2018253224","https://openalex.org/W333749553","https://openalex.org/W1966623661","https://openalex.org/W2942288111","https://openalex.org/W2039516134","https://openalex.org/W108066508","https://openalex.org/W4250527476","https://openalex.org/W2029861847","https://openalex.org/W2046228374"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"$$\\mathbb{F}_q$$":[2],"<mml:math":[3,31,45,57,70,113,222],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[4,32,46,58,71,114,223],"<mml:msub>":[5],"<mml:mi>F</mml:mi>":[6,225],"<mml:mi>q</mml:mi>":[7,227],"</mml:msub>":[8],"</mml:math>":[9,38,51,64,77,192,231],"be":[10],"a":[11,205,213],"finite":[12],"field":[13],"of":[14,204,208,220],"characteristic":[15],"p":[16],".":[17],"In":[18],"this":[19,196],"paper":[20],"we":[21,194],"prove":[22],"that":[23],"the":[24,200,234],"c":[25,96,107,201],"-Boomerang":[26],"Uniformity,":[27],"$$c":[28],"\\ne":[29,87],"0$$":[30],"<mml:mrow>":[33,59,72,115,117,121,130,143,156,167,180,226],"<mml:mi>c</mml:mi>":[34,132,157,181],"<mml:mo>\u2260</mml:mo>":[35,135],"<mml:mn>0</mml:mn>":[36],"</mml:mrow>":[37,63,76,127,138,153,162,177,184,188,191,228],",":[39,52,78,232],"for":[40],"all":[41],"permutation":[42],"monomials":[43],"$$x^d$$":[44],"<mml:msup>":[47,122,131],"<mml:mi>x</mml:mi>":[48],"<mml:mi>d</mml:mi>":[49,60,75,123,145,148,169,172],"</mml:msup>":[50,125,134],"where":[53],"$$d":[54],"&gt;":[55],"1$$":[56],"<mml:mo>&gt;</mml:mo>":[61],"<mml:mn>1</mml:mn>":[62,136,150,160,183],"and":[65],"$$p":[66],"\\not":[67],"\\mid":[68],"d$$":[69],"<mml:mi>p</mml:mi>":[73],"<mml:mo>\u2224</mml:mo>":[74],"is":[79],"bounded":[80],"by":[81],"$$\\left\\{":[82],"\\begin{array}{ll}":[83],"d^2,":[84],"&amp;":[85,95,106],"c^2":[86],"1,":[88,99],"\\\\":[89,100],"d":[90,101],"\\cdot":[91,102],"(d":[92,103],"-":[93,98,104],"1),":[94],"=":[97,108],"2),":[105],"1":[109],"\\end{array}":[110],"\\right\\}":[111],".$$":[112],"<mml:mfenced>":[116],"<mml:mtable>":[118],"<mml:mtr>":[119,141,165],"<mml:mtd>":[120,129,142,155,166,179],"<mml:mn>2</mml:mn>":[124,133,174],"<mml:mo>,</mml:mo>":[126,137,152,161,176],"</mml:mtd>":[128,139,154,163,178,185],"</mml:mtr>":[140,164,186],"<mml:mrow/>":[144,168],"<mml:mo>\u00b7</mml:mo>":[146,170],"<mml:mo>(</mml:mo>":[147,171],"<mml:mo>-</mml:mo>":[149,159,173],"<mml:mo>)</mml:mo>":[151,175],"<mml:mo>=</mml:mo>":[158,182],"</mml:mtable>":[187],"</mml:mfenced>":[189],"<mml:mo>.</mml:mo>":[190],"Further,":[193],"utilize":[195],"bound":[197],"to":[198,216],"estimate":[199],"-boomerang":[202],"uniformity":[203],"large":[206],"class":[207],"generalized":[209],"triangular":[210],"dynamical":[211],"systems,":[212],"polynomial-based":[214],"approach":[215],"describe":[217],"cryptographic":[218],"permutations":[219],"$$\\mathbb{F}_{q}^{n}$$":[221],"<mml:msubsup>":[224],"<mml:mi>n</mml:mi>":[229],"</mml:msubsup>":[230],"including":[233],"well-known":[235],"substitution\u2013permutation":[236],"network.":[237]},"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}