{"id":"https://openalex.org/W4413221857","doi":"https://doi.org/10.1007/s12095-025-00833-3","title":"Pattern sets for $$\\mathbb {F}_q$$-sequences invariant under the continued fraction operator K (the Berlekamp-Massey algorithm)","display_name":"Pattern sets for $$\\mathbb {F}_q$$-sequences invariant under the continued fraction operator K (the Berlekamp-Massey algorithm)","publication_year":2025,"publication_date":"2025-08-11","ids":{"openalex":"https://openalex.org/W4413221857","doi":"https://doi.org/10.1007/s12095-025-00833-3"},"language":"en","primary_location":{"id":"doi:10.1007/s12095-025-00833-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-025-00833-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-025-00833-3.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"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":"Cryptography and Communications","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/s12095-025-00833-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047538216","display_name":"M\u00f3nica del Pilar Canales","orcid":null},"institutions":[{"id":"https://openalex.org/I4210112547","display_name":"Universidad del Alba","ror":"https://ror.org/01rwn3f68","country_code":"CL","type":"education","lineage":["https://openalex.org/I4210112547"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"M\u00f3nica\u00a0del\u00a0P. Canales","raw_affiliation_strings":["MATEMATICVM @matematicvm, Valdivia, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MATEMATICVM @matematicvm, Valdivia, Chile","institution_ids":["https://openalex.org/I4210112547"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078457305","display_name":"Shirley Cheung H.C.","orcid":null},"institutions":[{"id":"https://openalex.org/I16465266","display_name":"Austral University of Chile","ror":"https://ror.org/029ycp228","country_code":"CL","type":"education","lineage":["https://openalex.org/I16465266"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Sergio Jara\u00a0C.","raw_affiliation_strings":["Universidad Austral de Chile, Facultad de Ingenier\u00eda, Valdivia, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Austral de Chile, Facultad de Ingenier\u00eda, Valdivia, Chile","institution_ids":["https://openalex.org/I16465266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018374172","display_name":"Michael Vielhaber","orcid":"https://orcid.org/0000-0003-1590-729X"},"institutions":[{"id":"https://openalex.org/I4210091436","display_name":"Hochschule Bremerhaven","ror":"https://ror.org/001yqrb02","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210091436"]},{"id":"https://openalex.org/I4210116731","display_name":"Bremerhaven Economic Development (Germany)","ror":"https://ror.org/021gr0q06","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210116731"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Vielhaber","raw_affiliation_strings":["HS Bremerhaven,FB 2, Bremerhaven, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"HS Bremerhaven,FB 2, Bremerhaven, Germany","institution_ids":["https://openalex.org/I4210091436","https://openalex.org/I4210116731"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018374172"],"corresponding_institution_ids":["https://openalex.org/I4210091436","https://openalex.org/I4210116731"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.7312,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.87935318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"18","issue":"1","first_page":"153","last_page":"172"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/algorithm","display_name":"Algorithm","score":0.6474410891532898},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2863411009311676}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6474410891532898},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2863411009311676}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12095-025-00833-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-025-00833-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-025-00833-3.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"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":"Cryptography and Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12095-025-00833-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-025-00833-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-025-00833-3.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"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":"Cryptography and Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413221857.pdf","grobid_xml":"https://content.openalex.org/works/W4413221857.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1496170221","https://openalex.org/W1569612250","https://openalex.org/W2001756903","https://openalex.org/W2007092636","https://openalex.org/W2011157068","https://openalex.org/W2014083840","https://openalex.org/W2066202870","https://openalex.org/W2072251416","https://openalex.org/W2130129774","https://openalex.org/W2146561088","https://openalex.org/W2162442687","https://openalex.org/W2163925910","https://openalex.org/W2769853338","https://openalex.org/W3212977760","https://openalex.org/W4238159413","https://openalex.org/W4239091356","https://openalex.org/W4413221857"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W4409439182","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"show":[2],"that":[3,49,75],"for":[4,195,217],"all":[5,218],"infinite":[6],"sequences":[7],"$$s\\in":[8],"\\mathbb":[9,200,220],"{F}_q^\\omega":[10],"$$":[11],"<mml:math":[12,54,99,143,172,202,222,233,252],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[13,55,100,144,173,203,223,234,253],"<mml:mrow>":[14,56,58,65,101,103,106,115,145,149,159,174,177,186,204,224,235,254,257,266],"<mml:mi>s</mml:mi>":[15,60,108,148,158,176,185,241],"<mml:mo>\u2208</mml:mo>":[16,206,226],"<mml:msubsup>":[17],"<mml:mi>F</mml:mi>":[18,208],"<mml:mi>q</mml:mi>":[19],"<mml:mi>\u03c9</mml:mi>":[20],"</mml:msubsup>":[21],"</mml:mrow>":[22,62,69,72,110,112,119,122,154,162,164,180,191,193,214,228,243,260],"</mml:math>":[23,73,123,165,194,215,229,244],",":[24,74,93,216,245],"two":[25],"properties":[26],"are":[27],"preserved":[28,46],"under":[29],"forward":[30],"and":[31,230],"backward":[32],"application":[33],"of":[34,79,83,139],"the":[35,77,80,136],"continued":[36],"fraction":[37],"operator":[38],"K":[39],"(the":[40],"modified":[41],"Berlekamp-Massey":[42],"Algorithm).":[43],"The":[44,125],"first":[45],"property":[47,127],"is":[48],"if":[50,135],"$${\\text":[51,96],"{supp}}(s)\\subset":[52],"[r]_n$$":[53,98],"<mml:mtext>supp</mml:mtext>":[57,102],"<mml:mo>(</mml:mo>":[59,104,107,146,240],"<mml:mo>)</mml:mo>":[61,109,111,242],"<mml:mo>\u2282</mml:mo>":[63,113],"<mml:msub>":[64,114,147,157,175,184,207,255,264],"<mml:mo>[</mml:mo>":[66,116],"<mml:mi>r</mml:mi>":[67,117],"<mml:mo>]</mml:mo>":[68,118],"<mml:mi>n</mml:mi>":[70,120,151,161,179,188,225,259,268],"</mml:msub>":[71,121,155,163,181,192,213,261],"is,":[76],"positions":[78],"nonzero":[81],"elements":[82],"s":[84],"lie":[85],"in":[86],"a":[87,196],"certain":[88],"residue":[89],"class":[90],"modulo":[91],"n":[92],"then":[94,246],"also":[95,247],"{supp}}(\\textbf{K}(s))\\subset":[97],"<mml:mi>K</mml:mi>":[105,239],".":[124],"other":[126],"applies":[128],"only":[129],"to":[130],"fields":[131],"with":[132,167],"characteristic":[133],"two:":[134],"sequence":[137],"consists":[138],"symbol":[140],"pairs":[141],"$$(s_{2n-1},s_{2n}$$":[142],"<mml:mn>2</mml:mn>":[150,160,178,187,210,258,267],"<mml:mo>-</mml:mo>":[152,189,269],"<mml:mn>1</mml:mn>":[153,190],"<mml:mo>,</mml:mo>":[156],")":[166],"$$s_{2n}":[168],"=":[169,249],"\\alpha":[170,250],"s_{2n-1}$$":[171],"<mml:mo>=</mml:mo>":[182,238,262],"<mml:mi>\u03b1</mml:mi>":[183,205,263],"fixed":[197],"$$\\alpha":[198],"\\in":[199],"{F}_{2^k}$$":[201],"<mml:msup>":[209],"<mml:mi>k</mml:mi>":[211],"</mml:msup>":[212],"$$n\\in":[219],"{N}$$":[221],"<mml:mi>N</mml:mi>":[227],"$$t:=":[231],"\\textbf{K}(s)$$":[232],"<mml:mi>t</mml:mi>":[236,256,265],"<mml:mo>:</mml:mo>":[237],"$$t_{2n}":[248],"t_{2n-1}$$":[251],"<mml:mn>1</":[270]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}