{"id":"https://openalex.org/W4281255010","doi":"https://doi.org/10.1007/s10623-022-01051-1","title":"Some hypersurfaces over finite fields, minimal codes and secret sharing schemes","display_name":"Some hypersurfaces over finite fields, minimal codes and secret sharing schemes","publication_year":2022,"publication_date":"2022-05-21","ids":{"openalex":"https://openalex.org/W4281255010","doi":"https://doi.org/10.1007/s10623-022-01051-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-022-01051-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-022-01051-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01051-1.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01051-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029175598","display_name":"Angela Aguglia","orcid":"https://orcid.org/0000-0001-6854-8679"},"institutions":[{"id":"https://openalex.org/I68618741","display_name":"Polytechnic University of Bari","ror":"https://ror.org/03c44v465","country_code":"IT","type":"education","lineage":["https://openalex.org/I68618741"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Angela Aguglia","raw_affiliation_strings":["Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy","institution_ids":["https://openalex.org/I68618741"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025473446","display_name":"Michela Ceria","orcid":"https://orcid.org/0000-0001-6059-9930"},"institutions":[{"id":"https://openalex.org/I68618741","display_name":"Polytechnic University of Bari","ror":"https://ror.org/03c44v465","country_code":"IT","type":"education","lineage":["https://openalex.org/I68618741"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Michela Ceria","raw_affiliation_strings":["Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy","institution_ids":["https://openalex.org/I68618741"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075036741","display_name":"Luca Giuzzi","orcid":"https://orcid.org/0000-0003-3975-7281"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Giuzzi","raw_affiliation_strings":["DICATAM, University of Brescia, Via Branze 53, 25123, Brescia, Italy"],"affiliations":[{"raw_affiliation_string":"DICATAM, University of Brescia, Via Branze 53, 25123, Brescia, Italy","institution_ids":["https://openalex.org/I79940851"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029175598"],"corresponding_institution_ids":["https://openalex.org/I68618741"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.2776,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61464214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"90","issue":"6","first_page":"1503","last_page":"1519"},"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/T10237","display_name":"Cryptography and Data Security","score":0.987500011920929,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9853000044822693,"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/secret-sharing","display_name":"Secret sharing","score":0.8346199989318848},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.8262804746627808},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7250391244888306},{"id":"https://openalex.org/keywords/access-structure","display_name":"Access structure","score":0.6931496858596802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5549554824829102},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5539214611053467},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.5487492680549622},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4929032325744629},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4447437524795532},{"id":"https://openalex.org/keywords/secure-multi-party-computation","display_name":"Secure multi-party computation","score":0.4310768246650696},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3911372423171997},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2803201973438263},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.22536835074424744},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15441182255744934}],"concepts":[{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.8346199989318848},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8262804746627808},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7250391244888306},{"id":"https://openalex.org/C2778950925","wikidata":"https://www.wikidata.org/wiki/Q4672474","display_name":"Access structure","level":4,"score":0.6931496858596802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5549554824829102},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5539214611053467},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.5487492680549622},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4929032325744629},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4447437524795532},{"id":"https://openalex.org/C18396474","wikidata":"https://www.wikidata.org/wiki/Q2465888","display_name":"Secure multi-party computation","level":3,"score":0.4310768246650696},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3911372423171997},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2803201973438263},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.22536835074424744},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15441182255744934},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10623-022-01051-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-022-01051-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01051-1.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2105.14508","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.14508","pdf_url":"https://arxiv.org/pdf/2105.14508","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:iris.unibs.it:11379/558779","is_oa":true,"landing_page_url":"http://hdl.handle.net/11379/558779","pdf_url":null,"source":{"id":"https://openalex.org/S4306400804","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Brescia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10623-022-01051-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-022-01051-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01051-1.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G2573627744","display_name":null,"funder_award_id":"GNSAGA","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G3830323789","display_name":null,"funder_award_id":"INdAM","funder_id":"https://openalex.org/F4320334045","funder_display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281255010.pdf","grobid_xml":"https://content.openalex.org/works/W4281255010.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W190248387","https://openalex.org/W1533708960","https://openalex.org/W1574372628","https://openalex.org/W1578199253","https://openalex.org/W1901594696","https://openalex.org/W2034720960","https://openalex.org/W2120756519","https://openalex.org/W2163834165","https://openalex.org/W3008041837","https://openalex.org/W3079710803","https://openalex.org/W3130396539","https://openalex.org/W3134278399","https://openalex.org/W3141673911"],"related_works":["https://openalex.org/W1557783852","https://openalex.org/W1474916271","https://openalex.org/W3088939963","https://openalex.org/W2357761884","https://openalex.org/W2110815651","https://openalex.org/W2111019861","https://openalex.org/W2611818227","https://openalex.org/W2388761115","https://openalex.org/W2377000132","https://openalex.org/W2081647269"],"abstract_inverted_index":{"Abstract":[0],"Linear":[1],"error-correcting":[2],"codes":[3,64,75],"can":[4,120],"be":[5,79,122],"used":[6],"for":[7,71],"constructing":[8],"secret":[9,21,89,99],"sharing":[10,22,90,100],"schemes;":[11],"however,":[12],"finding":[13],"in":[14,25],"general":[15],"the":[16,36,84,88,98,112],"access":[17,29,85,117],"structures":[18,30,86],"of":[19,38,87,115],"these":[20,56,74],"schemes":[23,91,101],"and,":[24],"particular,":[26],"determining":[27],"efficient":[28],"is":[31,107],"difficult.":[32],"Here":[33],"we":[34,82],"investigate":[35],"properties":[37],"certain":[39],"algebraic":[40],"hypersurfaces":[41],"over":[42],"finite":[43],"fields,":[44],"whose":[45],"intersection":[46],"numbers":[47],"with":[48,65],"any":[49],"hyperplane":[50],"only":[51],"takes":[52],"a":[53],"few":[54],"values;":[55],"varieties":[57],"give":[58],"rise":[59],"to":[60,78,111],"q":[61,72],"-divisible":[62],"linear":[63],"at":[66],"most":[67],"5":[68],"weights.":[69],"Furthermore,":[70],"odd,":[73],"turn":[76],"out":[77],"minimal":[80,116],"and":[81,119],"characterize":[83],"based":[92],"on":[93],"their":[94],"dual":[95],"codes.":[96],"Indeed,":[97],"thus":[102],"obtained":[103],"are":[104],"democratic,":[105],"that":[106],"each":[108],"participant":[109],"belongs":[110],"same":[113],"number":[114],"sets":[118],"easily":[121],"described.":[123]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}