{"id":"https://openalex.org/W7223105271","doi":"https://doi.org/10.48550/arxiv.2610.28297","title":"Twisted group codes of dimension 2 and 3","display_name":"Twisted group codes of dimension 2 and 3","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223105271","doi":"https://doi.org/10.48550/arxiv.2610.28297"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28297","pdf_url":"https://arxiv.org/pdf/2610.28297","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/2610.28297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100718832","display_name":"\u00c1lvaro Otero S\u00e1nchez","orcid":"https://orcid.org/0009-0009-5613-2081","observed_orcids":["https://orcid.org/0009-0009-5613-2081"]},"institutions":[{"id":"https://openalex.org/I52354020","display_name":"University of Almer\u00eda","ror":"https://ror.org/003d3xx08","country_code":"ES","type":"education","lineage":["https://openalex.org/I52354020"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Sanchez, Alvaro Otero","raw_affiliation_strings":["Department of Mathematics , Universidad de Almer\u00eda , Almer\u00eda , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Universidad de Almer\u00eda , Almer\u00eda , Spain","institution_ids":["https://openalex.org/I52354020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100718832"],"corresponding_institution_ids":["https://openalex.org/I52354020"],"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":1.0,"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":1.0,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.0,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/permutation-equivalence","display_name":"permutation equivalence","score":0.9850000143051147},{"id":"https://openalex.org/keywords/trace-map","display_name":"trace map","score":0.8930000066757202},{"id":"https://openalex.org/keywords/griesmer-bound","display_name":"Griesmer bound","score":0.9929999709129333},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"minimum distance","score":0.8429999947547913},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.49300000071525574},{"id":"https://openalex.org/keywords/cyclic-codes","display_name":"cyclic codes","score":0.593999981880188}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7760999798774719},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.734499990940094},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6151000261306763},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.597100019454956},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5618000030517578},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.5342000126838684},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.47859999537467957},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4697999954223633},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4106000065803528},{"id":"https://openalex.org/C20295870","wikidata":"https://www.wikidata.org/wiki/Q5532500","display_name":"Generalized permutation matrix","level":4,"score":0.40369999408721924},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3955000042915344},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.3937999904155731},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.3928000032901764},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.37610000371932983},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C147073270","wikidata":"https://www.wikidata.org/wiki/Q567083","display_name":"Annihilator","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.2648000121116638},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.2581999897956848},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.2556999921798706},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28297","pdf_url":"https://arxiv.org/pdf/2610.28297","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.2610.28297","doi":"https://doi.org/10.48550/arxiv.2610.28297","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28297","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.28297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28297","pdf_url":"https://arxiv.org/pdf/2610.28297","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223105271.pdf","grobid_xml":"https://content.openalex.org/works/W7223105271.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7118316834","https://openalex.org/W3169477034","https://openalex.org/W3000823598","https://openalex.org/W7096614046","https://openalex.org/W7065027573","https://openalex.org/W2895839996","https://openalex.org/W423121922","https://openalex.org/W4410562697","https://openalex.org/W2165973477","https://openalex.org/W4320477810"],"abstract_inverted_index":{"It":[0],"is":[1,79,87],"known":[2],"that":[3,21],"all":[4],"group":[5,17,23,37,93,118],"codes":[6,24,110],"of":[7,25,57,82,107],"dimension":[8,26,125],"at":[9,27],"most":[10,28],"$3$":[11,29],"are":[12,30],"permutation":[13,67],"equivalent":[14,32,90],"to":[15,34,40,91],"abelian":[16,36],"codes.":[18],"We":[19],"prove":[20],"twisted":[22],"monomially":[31,89],"either":[33],"an":[35,41,80],"code":[38,53,119],"or":[39],"irreducible":[42,108],"constacyclic":[43,109],"code,":[44],"and":[45,69,105,124],"in":[46,102],"the":[47,52,70,76,113,121],"second":[48,71],"case":[49,72],"we":[50,97],"describe":[51],"explicitly":[54],"by":[55,66],"means":[56],"a":[58],"trace":[59],"map.":[60],"Monomial":[61],"equivalence":[62],"cannot":[63,73],"be":[64,74],"replaced":[65],"equivalence,":[68],"avoided:":[75],"ternary":[77],"tetracode":[78],"ideal":[81],"$\\mathbb":[83],"F_3[x]/(x^4+1)$":[84],"but":[85],"it":[86],"not":[88],"any":[92],"code.":[94],"More":[95],"generally,":[96],"give":[98],"two":[99],"infinite":[100],"families,":[101],"dimensions":[103],"$2$":[104],"$3$,":[106],"which":[111],"attain":[112],"Griesmer":[114],"bound,":[115],"whereas":[116],"every":[117],"with":[120],"same":[122],"length":[123],"has":[126],"smaller":[127],"minimum":[128],"distance.":[129]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-22T00:00:00"}