{"id":"https://openalex.org/W4410301501","doi":"https://doi.org/10.1007/s10623-025-01637-5","title":"Evaluation codes arising from symmetric polynomials","display_name":"Evaluation codes arising from symmetric polynomials","publication_year":2025,"publication_date":"2025-05-12","ids":{"openalex":"https://openalex.org/W4410301501","doi":"https://doi.org/10.1007/s10623-025-01637-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-025-01637-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01637-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01637-5.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":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01637-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011207459","display_name":"Barbara Gatti","orcid":null},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]},{"id":"https://openalex.org/I20272500","display_name":"University of Basilicata","ror":"https://ror.org/03tc05689","country_code":"IT","type":"education","lineage":["https://openalex.org/I20272500"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Barbara Gatti","raw_affiliation_strings":["Department of Mathematics and Physics \u201cEnnio de Giorgi\u201d, University of Salento, Via per Arnesano, 73100, Lecce, Italy","Department of Mathematics, Computer Science and Economics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics \u201cEnnio de Giorgi\u201d, University of Salento, Via per Arnesano, 73100, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Department of Mathematics, Computer Science and Economics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy","institution_ids":["https://openalex.org/I20272500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009919372","display_name":"G\u00e1bor Korchm\u00e1ros","orcid":"https://orcid.org/0000-0002-2776-5754"},"institutions":[{"id":"https://openalex.org/I20272500","display_name":"University of Basilicata","ror":"https://ror.org/03tc05689","country_code":"IT","type":"education","lineage":["https://openalex.org/I20272500"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"G\u00e1bor Korchm\u00e1ros","raw_affiliation_strings":["Department of Mathematics, Computer Science and Economics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Computer Science and Economics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy","institution_ids":["https://openalex.org/I20272500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067363487","display_name":"G\u00e1bor P. Nagy","orcid":"https://orcid.org/0000-0002-9558-4197"},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"G\u00e1bor P. Nagy","raw_affiliation_strings":["Bolyai Institute, University of Szeged, Aradi v\u00e9rtan\u00fak tere 1, Szeged, 6720, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bolyai Institute, University of Szeged, Aradi v\u00e9rtan\u00fak tere 1, Szeged, 6720, Hungary","institution_ids":["https://openalex.org/I227486990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010029041","display_name":"Vincenzo Pallozzi Lavorante","orcid":"https://orcid.org/0000-0002-8725-5473"},"institutions":[{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vincenzo Pallozzi Lavorante","raw_affiliation_strings":["Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA","institution_ids":["https://openalex.org/I2613432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114633629","display_name":"Gioia Schulte","orcid":null},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]},{"id":"https://openalex.org/I20272500","display_name":"University of Basilicata","ror":"https://ror.org/03tc05689","country_code":"IT","type":"education","lineage":["https://openalex.org/I20272500"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gioia Schulte","raw_affiliation_strings":["Department of Mathematics and Physics \u201cEnnio de Giorgi\u201d, University of Salento, Via per Arnesano, 73100, Lecce, Italy","Department of Mathematics, Computer Science and Economics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics \u201cEnnio de Giorgi\u201d, University of Salento, Via per Arnesano, 73100, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Department of Mathematics, Computer Science and Economics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy","institution_ids":["https://openalex.org/I20272500"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5009919372"],"corresponding_institution_ids":["https://openalex.org/I20272500"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04142524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"93","issue":"8","first_page":"3361","last_page":"3373"},"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":0.9961000084877014,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.8481485843658447},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5274983644485474},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.44777366518974304},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3942068815231323},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1763378083705902}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8481485843658447},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5274983644485474},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.44777366518974304},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3942068815231323},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1763378083705902}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10623-025-01637-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01637-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01637-5.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:publicatio.bibl.u-szeged.hu:37460","is_oa":true,"landing_page_url":"http://publicatio.bibl.u-szeged.hu/37460/1/GattiKorchmarosNagyLavoranteSchulteEvaluationcodesarisingfromsymmetricpolynomials2025.pdf","pdf_url":"http://publicatio.bibl.u-szeged.hu/37460/7/36149920.pdf","source":{"id":"https://openalex.org/S4306400675","display_name":"SZTE Publicatio Repozit\u00f3rium (University of Szeged)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I227486990","host_organization_name":"University of Szeged","host_organization_lineage":["https://openalex.org/I227486990"],"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":"PeerReviewed"}],"best_oa_location":{"id":"doi:10.1007/s10623-025-01637-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01637-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01637-5.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":[],"awards":[{"id":"https://openalex.org/G631101471","display_name":"SaTC: CORE: Small: Applications of Galois Theory to the Search for Non-Linear Functions","funder_award_id":"2127742","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320327745","display_name":"Universit\u00e0 degli Studi della Basilicata","ror":"https://ror.org/03tc05689"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410301501.pdf","grobid_xml":"https://content.openalex.org/works/W4410301501.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1707592146","https://openalex.org/W2039270103","https://openalex.org/W2324880469","https://openalex.org/W4304142904","https://openalex.org/W4385210693","https://openalex.org/W4403395753","https://openalex.org/W4405834031"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"Datta":[1],"and":[2],"Johnsen":[3],"(Des":[4],"Codes":[5],"Cryptogr":[6],"91:747\u2013761,":[7],"2023)":[8],"introduced":[9],"a":[10,32,68],"new":[11],"family":[12],"of":[13,20,47,56,76,83],"evaluation":[14],"codes":[15,101],"in":[16],"an":[17],"affine":[18],"space":[19],"dimension":[21],"$$\\ge":[22],"2$$":[23],"<mml:math":[24,37,85,105],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[25,38,86,106],"<mml:mrow>":[26,87,113],"<mml:mo>\u2265</mml:mo>":[27],"<mml:mn>2</mml:mn>":[28,110],"</mml:mrow>":[29,93,119],"</mml:math>":[30,43,94,125],"over":[31],"finite":[33],"field":[34],"$${\\mathbb":[35],"{F}}_q$$":[36],"<mml:msub>":[39],"<mml:mi>F</mml:mi>":[40],"<mml:mi>q</mml:mi>":[41,88,112,115],"</mml:msub>":[42],"where":[44],"linear":[45,74],"combinations":[46],"elementary":[48],"symmetric":[49,77],"polynomials":[50],"are":[51],"evaluated":[52],"on":[53],"the":[54,132],"set":[55],"all":[57],"points":[58],"with":[59],"pairwise":[60],"distinct":[61],"coordinates.":[62],"In":[63],"this":[64],"paper,":[65],"we":[66],"propose":[67],"generalization":[69],"by":[70],"taking":[71],"low":[72],"dimensional":[73],"systems":[75],"polynomials.":[78],"Computation":[79],"for":[80],"small":[81],"values":[82],"$$q=7,9$$":[84],"<mml:mo>=</mml:mo>":[89],"<mml:mn>7</mml:mn>":[90],"<mml:mo>,</mml:mo>":[91,120,122],"<mml:mn>9</mml:mn>":[92],"shows":[95],"that":[96],"carefully":[97],"chosen":[98],"generalized":[99],"Datta\u2013Johnsen":[100],"$$\\left[":[102],"\\frac{1}{2}q(q-1),3,d\\right]":[103],"$$":[104],"<mml:mfenced>":[107],"<mml:mfrac>":[108],"<mml:mn>1</mml:mn>":[109,117],"</mml:mfrac>":[111],"<mml:mo>(</mml:mo>":[114],"<mml:mo>-</mml:mo>":[116],"<mml:mo>)</mml:mo>":[118],"<mml:mn>3</mml:mn>":[121],"<mml:mi>d</mml:mi>":[123],"</mml:mfenced>":[124],"have":[126],"minimum":[127],"distance":[128],"d":[129],"equal":[130],"to":[131],"optimal":[133],"value":[134],"minus":[135],"1.":[136]},"counts_by_year":[],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-05-13T00:00:00"}