{"id":"https://openalex.org/W7204840502","doi":"https://doi.org/10.48550/arxiv.2608.27565","title":"Spectral Theory of Semisimple Bivariate Bicycle Codes","display_name":"Spectral Theory of Semisimple Bivariate Bicycle Codes","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204840502","doi":"https://doi.org/10.48550/arxiv.2608.27565"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27565","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27565","pdf_url":"https://arxiv.org/pdf/2608.27565","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/2608.27565","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015648121","display_name":"Eric Sabo","orcid":"https://orcid.org/0000-0002-0998-6107","observed_orcids":["https://orcid.org/0000-0002-0998-6107"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sabo, Eric","raw_affiliation_strings":["1 Xanadu , Toronto , Ontario M5G 2C8 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1 Xanadu , Toronto , Ontario M5G 2C8 , Canada","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036635471","display_name":"Mahir Bilen Can","orcid":"https://orcid.org/0000-0002-0175-4897","observed_orcids":["https://orcid.org/0000-0002-0175-4897"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Can, Mahir Bilen","raw_affiliation_strings":["1 Xanadu , Toronto , Ontario M5G 2C8 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1 Xanadu , Toronto , Ontario M5G 2C8 , Canada","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111743134","display_name":"David Marquis","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marquis, David","raw_affiliation_strings":["1 Xanadu , Toronto , Ontario M5G 2C8 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1 Xanadu , Toronto , Ontario M5G 2C8 , Canada","institution_ids":[]}]}],"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":3,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.0,"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/bivariate-bicycle-codes","display_name":"bivariate bicycle codes","score":0.9539999961853027},{"id":"https://openalex.org/keywords/minimum-distance-bounds","display_name":"minimum distance bounds","score":0.925000011920929},{"id":"https://openalex.org/keywords/bch-codes","display_name":"BCH codes","score":0.7620000243186951},{"id":"https://openalex.org/keywords/product-construction","display_name":"product construction","score":0.734000027179718},{"id":"https://openalex.org/keywords/algebraic-coding-theory","display_name":"algebraic coding theory","score":0.7670000195503235}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7405999898910522},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6316999793052673},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5407000184059143},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47600001096725464},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47350001335144043},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.44209998846054077},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4205999970436096},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3880000114440918},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.35370001196861267},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.3009999990463257},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2996000051498413},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.26829999685287476},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27565","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27565","pdf_url":"https://arxiv.org/pdf/2608.27565","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.2608.27565","doi":"https://doi.org/10.48550/arxiv.2608.27565","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27565","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.27565","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27565","pdf_url":"https://arxiv.org/pdf/2608.27565","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/W7204840502.pdf","grobid_xml":"https://content.openalex.org/works/W7204840502.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4402703561","https://openalex.org/W4415085803","https://openalex.org/W4416243483","https://openalex.org/W7168237569","https://openalex.org/W7172257030"],"related_works":["https://openalex.org/W7168237569","https://openalex.org/W7215080573","https://openalex.org/W7212024023","https://openalex.org/W7007745908","https://openalex.org/W7161261135","https://openalex.org/W7202166307","https://openalex.org/W7163993547","https://openalex.org/W6948064834","https://openalex.org/W4416363943","https://openalex.org/W6885115682"],"abstract_inverted_index":{"Extending":[0],"the":[1,71],"classical":[2],"theory":[3,36],"of":[4,37,48],"two-dimensional":[5],"cyclic":[6],"codes,":[7],"we":[8],"develop":[9],"an":[10],"algebraic":[11],"approach":[12],"to":[13,42,56,73],"bivariate":[14],"bicycle":[15],"codes.":[16],"Using":[17],"Frobenius-orbit":[18],"idempotents,":[19],"formulas":[20],"for":[21],"logical":[22],"dimensions":[23],"are":[24,32],"derived":[25],"and":[26],"lower":[27],"bounds":[28],"on":[29,65],"minimum":[30],"distances":[31],"established.":[33],"A":[34],"systematic":[35],"code":[38],"symmetries":[39],"is":[40],"formulated":[41],"construct":[43],"a":[44],"structured":[45],"block-monomial":[46],"subgroup":[47],"coordinate":[49],"permutations.":[50],"Several":[51],"explicit":[52],"examples":[53],"show":[54],"how":[55],"generate":[57],"these":[58],"codes":[59],"from":[60],"first":[61],"principles":[62],"without":[63],"relying":[64],"numerical":[66],"searches.":[67],"An":[68],"appendix":[69],"extends":[70],"analysis":[72],"BCH-based":[74],"product":[75],"constructions.":[76]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}