{"id":"https://openalex.org/W7147195128","doi":"https://doi.org/10.48550/arxiv.2603.29150","title":"A Structural Characterization of Cyclotomic Cosets with Applications to Affine-Invariant Codes and BCH Codes","display_name":"A Structural Characterization of Cyclotomic Cosets with Applications to Affine-Invariant Codes and BCH Codes","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7147195128","doi":"https://doi.org/10.48550/arxiv.2603.29150"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.29150","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29150","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":null,"license_id":null,"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.2603.29150","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132565604","display_name":"Xiongkun Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Xiongkun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072537287","display_name":"Dabin Zheng","orcid":"https://orcid.org/0000-0003-3947-1590"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Dabin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132672979","display_name":"Xiaoqiang Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Xiaoqiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132678391","display_name":"Mu Yuan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuan, Mu","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/T11130","display_name":"Coding theory and cryptography","score":0.9556000232696533,"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":0.9556000232696533,"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":0.03530000150203705,"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/T10849","display_name":"Finite Group Theory Research","score":0.004100000020116568,"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/bch-code","display_name":"BCH code","score":0.9122999906539917},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.7264000177383423},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.49729999899864197},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.49459999799728394},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.489300012588501},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.4092000126838684},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4047999978065491},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.385699987411499}],"concepts":[{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.9122999906539917},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.7264000177383423},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.65420001745224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5659000277519226},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.49729999899864197},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49459999799728394},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4050999879837036},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4047999978065491},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.36010000109672546},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.31940001249313354},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.29809999465942383},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.29600000381469727},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C78065487","wikidata":"https://www.wikidata.org/wiki/Q1061598","display_name":"Reed\u2013Solomon error correction","level":5,"score":0.26980000734329224},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.25949999690055847}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.29150","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29150","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.29150","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29150","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Affine-invariant":[0],"codes":[1,25,92,117,122,135,188],"have":[2],"attracted":[3],"considerable":[4],"attention":[5],"due":[6],"to":[7],"their":[8,94,108,124,190],"rich":[9],"algebraic":[10],"structure":[11],"and":[12,93,98,123,147,158,172,178,189],"strong":[13],"theoretical":[14],"properties.":[15],"In":[16,110],"this":[17,79],"paper,":[18],"we":[19,51,81,99,153],"study":[20,73],"a":[21,40,53],"family":[22],"of":[23,30,33,39,62,68,74,88,107,131,186],"affine-invariant":[24,91],"whose":[26],"defining":[27],"set":[28],"consists":[29],"all":[31],"descendants":[32],"elements":[34],"in":[35,71],"the":[36,60,72,86,89,104,128,164,183],"cyclotomic":[37,75],"coset":[38],"single":[41],"specified":[42],"element.":[43],"Our":[44],"main":[45],"contributions":[46],"are":[47],"as":[48],"follows.":[49],"First,":[50],"establish":[52,100],"new":[54],"combinatorial":[55],"result":[56],"that":[57],"determines":[58],"exactly":[59],"size":[61],"such":[63],"descendant":[64],"sets,":[65],"which":[66],"is":[67],"independent":[69],"interest":[70],"cosets.":[76],"Second,":[77],"using":[78],"result,":[80],"derive":[82],"explicit":[83],"formulas":[84,157],"for":[85,182],"dimensions":[87],"corresponding":[90],"associated":[95],"cyclic":[96],"codes,":[97],"lower":[101,161],"bounds":[102],"on":[103,163],"minimum":[105,165],"distances":[106],"duals.":[109,191],"particular,":[111],"under":[112],"appropriate":[113],"parameter":[114],"choices,":[115],"these":[116],"yield":[118],"narrow-sense":[119,132],"primitive":[120,133],"BCH":[121,134,187],"extended":[125],"counterparts.":[126],"For":[127],"special":[129],"class":[130],"with":[136],"designed":[137],"distance":[138],"$\u03b4=":[139],"(b+1)q^{m-t-1}$,":[140],"where":[141],"$1":[142],"\\leq":[143,145,149,151],"b":[144],"q-1$":[146],"$0":[148],"t":[150],"m-1$,":[152],"provide":[154,179],"exact":[155],"dimension":[156],"an":[159],"improved":[160],"bound":[162],"distance.":[166],"The":[167],"results":[168],"presented":[169],"here":[170],"extend":[171],"sharpen":[173],"several":[174],"previously":[175],"known":[176],"results,":[177],"refined":[180],"tools":[181],"parametric":[184],"analysis":[185]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-02T00:00:00"}