{"id":"https://openalex.org/W7160980807","doi":"https://doi.org/10.48550/arxiv.2605.12295","title":"Symmetric Tensor Decompositions over Finite Fields","display_name":"Symmetric Tensor Decompositions over Finite Fields","publication_year":2026,"publication_date":"2026-05-12","ids":{"openalex":"https://openalex.org/W7160980807","doi":"https://doi.org/10.48550/arxiv.2605.12295"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.12295","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12295","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.12295","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026871112","display_name":"Giuseppe Cotardo","orcid":"https://orcid.org/0000-0001-9178-3941"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cotardo, Giuseppe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041162879","display_name":"Ferdinando Zullo","orcid":"https://orcid.org/0000-0002-5087-2363"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zullo, Ferdinando","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.5127000212669373,"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":0.5127000212669373,"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/T12303","display_name":"Tensor decomposition and applications","score":0.1768999993801117,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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":0.1746000051498413,"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/symmetric-tensor","display_name":"Symmetric tensor","score":0.7979000210762024},{"id":"https://openalex.org/keywords/symmetric-bilinear-form","display_name":"Symmetric bilinear form","score":0.710099995136261},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6552000045776367},{"id":"https://openalex.org/keywords/ring-of-symmetric-functions","display_name":"Ring of symmetric functions","score":0.6481000185012817},{"id":"https://openalex.org/keywords/complete-homogeneous-symmetric-polynomial","display_name":"Complete homogeneous symmetric polynomial","score":0.5999000072479248},{"id":"https://openalex.org/keywords/power-sum-symmetric-polynomial","display_name":"Power sum symmetric polynomial","score":0.545199990272522},{"id":"https://openalex.org/keywords/tensor-field","display_name":"Tensor field","score":0.522599995136261},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5145999789237976},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.5033000111579895}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8184999823570251},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.7979000210762024},{"id":"https://openalex.org/C79940087","wikidata":"https://www.wikidata.org/wiki/Q2100018","display_name":"Symmetric bilinear form","level":3,"score":0.710099995136261},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6552000045776367},{"id":"https://openalex.org/C156903151","wikidata":"https://www.wikidata.org/wiki/Q17102788","display_name":"Ring of symmetric functions","level":4,"score":0.6481000185012817},{"id":"https://openalex.org/C171436396","wikidata":"https://www.wikidata.org/wiki/Q5156499","display_name":"Complete homogeneous symmetric polynomial","level":5,"score":0.5999000072479248},{"id":"https://openalex.org/C129010115","wikidata":"https://www.wikidata.org/wiki/Q1298683","display_name":"Power sum symmetric polynomial","level":5,"score":0.545199990272522},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.522599995136261},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5145999789237976},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.5033000111579895},{"id":"https://openalex.org/C109385661","wikidata":"https://www.wikidata.org/wiki/Q11358307","display_name":"Triple system","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C64338288","wikidata":"https://www.wikidata.org/wiki/Q2235316","display_name":"Elementary symmetric polynomial","level":4,"score":0.4535999894142151},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.44020000100135803},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4237000048160553},{"id":"https://openalex.org/C167552581","wikidata":"https://www.wikidata.org/wiki/Q194221","display_name":"Symmetric closure","level":5,"score":0.4090999960899353},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.38830000162124634},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3652999997138977},{"id":"https://openalex.org/C148125525","wikidata":"https://www.wikidata.org/wiki/Q904927","display_name":"Tensor density","level":4,"score":0.3506999909877777},{"id":"https://openalex.org/C52153879","wikidata":"https://www.wikidata.org/wiki/Q930499","display_name":"Symmetric polynomial","level":4,"score":0.34630000591278076},{"id":"https://openalex.org/C64835786","wikidata":"https://www.wikidata.org/wiki/Q17004583","display_name":"Cartesian tensor","level":5,"score":0.3441999852657318},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C78136718","wikidata":"https://www.wikidata.org/wiki/Q7600073","display_name":"Stanley symmetric function","level":5,"score":0.3089999854564667},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.30809998512268066},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C93776189","wikidata":"https://www.wikidata.org/wiki/Q1404488","display_name":"Tensor product of Hilbert spaces","level":4,"score":0.2777999937534332},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26989999413490295},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.12295","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12295","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.12295","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12295","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,45,90],"study":[1],"the":[2,59,74,93,105,119,124],"symmetric":[3,18,24,28,31,42,75,85,94,98,120],"tensor":[4,32,121],"rank":[5,122],"of":[6,73,96,123],"multiplication":[7,125],"over":[8,54],"finite":[9,55,112],"field":[10,16,113],"extensions":[11],"using":[12],"linearized":[13,19,43],"polynomials.":[14,44],"Via":[15],"trace,":[17],"polynomials":[20],"are":[21],"identified":[22],"with":[23,111,118],"bilinear":[25,76],"forms":[26],"and":[27,57,82,101],"matrices,":[29],"allowing":[30],"decompositions":[33,86],"to":[34,62],"be":[35],"reformulated":[36],"as":[37],"spanning":[38,48],"problems":[39],"by":[40],"rank-one":[41],"translate":[46],"these":[47],"conditions":[49],"into":[50],"explicit":[51,84],"linear":[52],"systems":[53],"fields":[56],"use":[58],"Frobenius":[60],"automorphism":[61],"obtain":[63,83],"computationally":[64],"effective":[65],"criteria.":[66],"As":[67],"applications,":[68],"we":[69],"recover":[70],"known":[71],"values":[72],"complexity":[77],"for":[78,87,104],"small":[79],"extension":[80],"degrees":[81],"several":[88],"parameters.":[89],"also":[91],"introduce":[92],"tensor-rank":[95],"a":[97],"rank-metric":[99],"code":[100,109],"show":[102],"that,":[103],"natural":[106],"one-dimensional":[107],"Gabidulin":[108],"associated":[110],"multiplication,":[114],"this":[115],"invariant":[116],"coincides":[117],"map.":[126]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-14T00:00:00"}