{"id":"https://openalex.org/W7165164664","doi":"https://doi.org/10.48550/arxiv.2606.18662","title":"On (Non-)Isomorphism of Self-Dual Lattices and Codes","display_name":"On (Non-)Isomorphism of Self-Dual Lattices and Codes","publication_year":2026,"publication_date":"2026-06-17","ids":{"openalex":"https://openalex.org/W7165164664","doi":"https://doi.org/10.48550/arxiv.2606.18662"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.18662","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18662","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.18662","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047830282","display_name":"Huck Bennett","orcid":"https://orcid.org/0000-0002-5469-8841"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bennett, Huck","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003183998","display_name":"Kyle Fridberg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fridberg, Kyle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10237","display_name":"Cryptography and Data Security","score":0.9190000295639038,"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/T10237","display_name":"Cryptography and Data Security","score":0.9190000295639038,"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/T11130","display_name":"Coding theory and cryptography","score":0.025699999183416367,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.00989999994635582,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/lattice","display_name":"Lattice (music)","score":0.6022999882698059},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.4147999882698059},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4133000075817108},{"id":"https://openalex.org/keywords/map-of-lattices","display_name":"Map of lattices","score":0.39969998598098755},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.3698999881744385},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.3334999978542328},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.3276999890804291}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6225000023841858},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6022999882698059},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44530001282691956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4268999993801117},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.4147999882698059},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C128379363","wikidata":"https://www.wikidata.org/wiki/Q6753757","display_name":"Map of lattices","level":4,"score":0.39969998598098755},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.3698999881744385},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.3334999978542328},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C201640847","wikidata":"https://www.wikidata.org/wiki/Q2362924","display_name":"Complete lattice","level":3,"score":0.28380000591278076},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C33884865","wikidata":"https://www.wikidata.org/wiki/Q1254335","display_name":"Cryptographic protocol","level":3,"score":0.271699994802475},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.18662","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18662","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.18662","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18662","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"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":{"A":[0],"recent":[1,65],"line":[2,190],"of":[3,13,59,71,93,102,117,131,191,216,254],"work":[4,66,192],"motivated":[5],"by":[6,193],"cryptographic":[7],"applications":[8],"has":[9,163],"studied":[10],"the":[11,14,69,82,86,112],"complexity":[12],"Lattice":[15],"Isomorphism":[16],"Problem":[17],"(LIP).":[18],"In":[19,80],"this":[20],"work,":[21],"we":[22,233],"study":[23,224],"LIP":[24,48,54],"on":[25,55,67,197,229,245],"self-dual":[26,60,132,150,230],"lattices":[27,133,198],"$\\cal{L}":[28,134],"\\subset":[29,135],"\\mathbb{R}^n$,":[30],"which":[31,260],"appear":[32],"naturally":[33],"in":[34],"many":[35],"applications.":[36],"Our":[37,124,186],"main":[38],"results":[39,63,125,187],"are":[40],"a":[41,50,56,74,189,209,213,240,251],"$2^{n/2":[42,87],"+":[43,88],"o(n)}$-time":[44,89],"randomized":[45],"algorithm":[46,242],"for":[47,53,91,148,175,243,259],"and":[49,97,101,157,195,204,232],"$\\mathsf{coNP}$":[51],"protocol":[52],"broad":[57],"class":[58,253],"lattices.":[61],"These":[62],"extend":[64],"ZLIP,":[68],"problem":[70],"deciding":[72],"whether":[73],"lattice":[75,140,151,161],"is":[76,142,262],"isomorphic":[77,143],"to":[78,144,212],"$\\mathbb{Z}^n$.":[79],"particular,":[81],"former":[83],"result":[84,110,116],"extends":[85,111],"algorithms":[90],"ZLIP":[92],"Bennett,":[94],"Ganju,":[95],"Peetathawachai,":[96],"Stephens-Davidowitz":[98],"(Eurocrypt,":[99],"2023)":[100],"Ducas":[103],"(Des.":[104],"Codes":[105],"Cryptogr.,":[106],"2024).":[107,123],"The":[108],"latter":[109],"$\\mathrm{ZLIP}":[113],"\\in":[114,171,178],"\\mathsf{coNP}$":[115],"Hunkenschr\u00f6der":[118],"(Math.":[119,218],"Prog.":[120],"Series":[121],"A,":[122],"leverage":[126],"two":[127],"key":[128],"structural":[129,237],"properties":[130,238],"\\mathbb{R}^n$:":[136],"(1)":[137],"every":[138,159,176],"such":[139,160,173,247],"$\\cal{L}$":[141,162],"$\\cal{L}_0":[145],"\\oplus":[146],"\\mathbb{Z}^r$":[147],"some":[149],"$\\cal{L}_0$":[152],"with":[153,199,256],"$\u03bb_1(\\cal{L}_0)^2":[154],"\\geq":[155],"2$,":[156],"(2)":[158],"\\emph{characteristic":[164],"vectors},":[165],"i.e.,":[166],"there":[167],"exist":[168],"vectors":[169],"$\\mathbf{w}":[170],"\\cal{L}$":[172],"that":[174,235],"$\\mathbf{v}":[177],"\\cal{L}$,":[179],"$\\langle\\mathbf{v},":[180],"\\mathbf{w}\\rangle":[181],"\\equiv":[182],"\\langle\\mathbf{v},":[183],"\\mathbf{v}\\rangle":[184],"\\pmod{2}$.":[185],"use":[188],"Elkies":[194,217],"Gaulter":[196],"long":[200],"shortest":[201],"characteristic":[202],"vectors,":[203],"can":[205],"be":[206],"strengthened":[207],"assuming":[208],"positive":[210],"answer":[211],"related":[214],"question":[215],"Res.":[219],"Lett.,":[220],"1995).":[221],"We":[222],"also":[223],"Permutation":[225],"Code":[226],"Equivalence":[227],"(PCE)":[228],"codes,":[231],"observe":[234],"similar":[236],"imply":[239],"polynomial-time":[241],"PCE":[244,261],"certain":[246],"codes.":[248],"This":[249],"gives":[250],"natural":[252],"codes":[255],"large":[257],"hull":[258],"easy.":[263]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-19T00:00:00"}
