{"id":"https://openalex.org/W7220741502","doi":"https://doi.org/10.48550/arxiv.2610.04856","title":"Code Equivalence and Automorphism Groups of Weighted Superelliptic Codes","display_name":"Code Equivalence and Automorphism Groups of Weighted Superelliptic Codes","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220741502","doi":"https://doi.org/10.48550/arxiv.2610.04856"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04856","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04856","pdf_url":"https://arxiv.org/pdf/2610.04856","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.04856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033168795","display_name":"Lubjana Beshaj","orcid":"https://orcid.org/0000-0002-4380-7483","observed_orcids":["https://orcid.org/0000-0002-4380-7483"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Beshaj, Lubjana","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066894707","display_name":"Tony Shaska","orcid":"https://orcid.org/0000-0002-2293-8230","observed_orcids":["https://orcid.org/0000-0002-2293-8230"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shaska, Tony","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":true,"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":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.00019999999494757503,"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/one-point-codes","display_name":"one-point codes","score":0.8399999737739563},{"id":"https://openalex.org/keywords/permutation-equivalence","display_name":"permutation equivalence","score":0.9160000085830688},{"id":"https://openalex.org/keywords/automorphism-groups","display_name":"automorphism groups","score":0.8659999966621399},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"minimum distance","score":0.7639999985694885},{"id":"https://openalex.org/keywords/regular-actions","display_name":"regular actions","score":0.43799999356269836},{"id":"https://openalex.org/keywords/hull-dimensions","display_name":"hull dimensions","score":0.7170000076293945}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8596000075340271},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.761900007724762},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6478999853134155},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6262999773025513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4823000133037567},{"id":"https://openalex.org/C75174853","wikidata":"https://www.wikidata.org/wiki/Q190629","display_name":"Centralizer and normalizer","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4115999937057495},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.4059000015258789},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.4004000127315521},{"id":"https://openalex.org/C7619685","wikidata":"https://www.wikidata.org/wiki/Q3630548","display_name":"Outer automorphism group","level":4,"score":0.3862000107765198},{"id":"https://openalex.org/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.38609999418258667},{"id":"https://openalex.org/C128489963","wikidata":"https://www.wikidata.org/wiki/Q1187724","display_name":"Filtration (mathematics)","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3695000112056732},{"id":"https://openalex.org/C90685605","wikidata":"https://www.wikidata.org/wiki/Q764115","display_name":"Projective line","level":4,"score":0.36640000343322754},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.31119999289512634},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.3001999855041504},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.29120001196861267},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.2904999852180481},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.28760001063346863},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.27810001373291016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2678999900817871},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04856","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04856","pdf_url":"https://arxiv.org/pdf/2610.04856","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,"listed_in":[],"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":"doi:10.48550/arxiv.2610.04856","doi":"https://doi.org/10.48550/arxiv.2610.04856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04856","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,"listed_in":[],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.04856","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04856","pdf_url":"https://arxiv.org/pdf/2610.04856","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220741502.pdf","grobid_xml":"https://content.openalex.org/works/W7220741502.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4415367495","https://openalex.org/W7172540279"],"related_works":["https://openalex.org/W7172540279","https://openalex.org/W7214107408","https://openalex.org/W1970232797","https://openalex.org/W2118302688","https://openalex.org/W2578644413","https://openalex.org/W2299401361","https://openalex.org/W2149503976","https://openalex.org/W2048655145","https://openalex.org/W3142083286","https://openalex.org/W2176253146"],"abstract_inverted_index":{"We":[0,41,100],"study":[1],"permutation":[2,55,77,104],"and":[3,33,37,51,56,71,87,116,159,167,195],"monomial":[4,45,57,165],"equivalence":[5],"for":[6,122],"one-point":[7],"codes":[8,28,32],"on":[9,20,63,144],"weighted":[10],"superelliptic":[11],"curves.":[12],"On":[13],"strata":[14],"where":[15],"$H_m\\simeq":[16],"\\Z/n\\Z\\times\\Z/m\\Z$":[17],"acts":[18],"regularly":[19],"the":[21,43,48,53,60,64,75,81,88,102,111,114,130,142,150,169,174,181,191],"evaluation":[22],"set,":[23],"we":[24,189],"prove":[25],"that":[26,156,168],"these":[27],"are":[29],"Cartesian":[30],"character":[31],"determine":[34,101,164,180,190],"their":[35],"primal":[36],"dual":[38],"minimum":[39],"distances.":[40],"compute":[42],"projective":[44],"normalizer":[46],"of":[47,80,113],"regular":[49,89,146,175],"action":[50,90],"classify":[52],"compatible":[54],"equivalences":[58],"through":[59],"induced":[61],"actions":[62],"defining":[65],"sets.":[66],"When":[67],"$d":[68],">":[69],"n$":[70],"$m":[72],"\\geq":[73],"2$,":[74],"common":[76],"automorphism":[78,105,176],"group":[79,106],"full":[82,103],"filtration":[83,115],"is":[84,139],"exactly":[85],"$H_m$,":[86],"can":[91],"be":[92],"recovered":[93],"from":[94,149],"its":[95],"two":[96],"lowest":[97],"nonconstant":[98],"members.":[99],"in":[107,129,199],"closed":[108],"form":[109],"at":[110],"top":[112],"give":[117],"a":[118],"field-independent":[119],"finite":[120],"certificate":[121],"$\\PAut":[123],"(":[124],"\\CC_s":[125],")":[126],"=":[127],"H_m$":[128],"remaining":[131],"primitive":[132],"cases":[133],"treated":[134],"here.":[135],"The":[136],"hull":[137,160,170],"dimension":[138,161],"bounded":[140],"by":[141],"genus":[143],"every":[145],"stratum,":[147],"apart":[148],"type":[151],"$(3,3,3)$.":[152],"Explicit":[153],"examples":[154],"show":[155],"length,":[157],"dimension,":[158],"do":[162],"not":[163,179],"equivalence,":[166],"profile":[171],"together":[172],"with":[173],"subgroup":[177],"does":[178],"curve":[182],"up":[183],"to":[184],"isomorphism.":[185],"As":[186],"an":[187],"application,":[188],"corresponding":[192],"hull-based":[193],"invariants":[194],"punctured":[196],"signatures":[197],"used":[198],"support-splitting":[200],"methods.":[201]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}