{"id":"https://openalex.org/W7140168041","doi":"https://doi.org/10.48550/arxiv.2603.20298","title":"Error-detecting solid codes","display_name":"Error-detecting solid codes","publication_year":2026,"publication_date":"2026-03-19","ids":{"openalex":"https://openalex.org/W7140168041","doi":"https://doi.org/10.48550/arxiv.2603.20298"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2603.20298","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.20298","pdf_url":"https://arxiv.org/pdf/2603.20298","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/2603.20298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023527819","display_name":"Nathan Thomas Carruth","orcid":"https://orcid.org/0000-0001-8026-6084","observed_orcids":["https://orcid.org/0000-0001-8026-6084"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carruth, Nathan Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5023527819"],"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":0.9375,"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":0.9375,"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/T11269","display_name":"Algorithms and Data Compression","score":0.043299999088048935,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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":0.01510000042617321,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/error-detection","display_name":"error detection","score":0.7720000147819519},{"id":"https://openalex.org/keywords/variable-length-coding","display_name":"variable-length codes","score":0.9259999990463257},{"id":"https://openalex.org/keywords/binary-codes","display_name":"binary codes","score":0.871999979019165},{"id":"https://openalex.org/keywords/code-construction","display_name":"code construction","score":0.5490000247955322}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5088000297546387},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5020999908447266},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4869999885559082},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.48669999837875366},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.459199994802475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4544999897480011},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4198000133037567},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41589999198913574},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.39259999990463257},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.38679999113082886},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.3709000051021576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34950000047683716},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33899998664855957},{"id":"https://openalex.org/C32795469","wikidata":"https://www.wikidata.org/wiki/Q5156430","display_name":"Complementary sequences","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2637999951839447},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2603.20298","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.20298","pdf_url":"https://arxiv.org/pdf/2603.20298","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.2603.20298","doi":"https://doi.org/10.48550/arxiv.2603.20298","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20298","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:2603.20298","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.20298","pdf_url":"https://arxiv.org/pdf/2603.20298","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/W7140168041.pdf","grobid_xml":"https://content.openalex.org/works/W7140168041.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3172060057","https://openalex.org/W2402317645","https://openalex.org/W2317163511","https://openalex.org/W3200876187","https://openalex.org/W2041249711","https://openalex.org/W992945056","https://openalex.org/W181254731","https://openalex.org/W601319811","https://openalex.org/W2747067170","https://openalex.org/W1985895929"],"abstract_inverted_index":{"A":[0],"code":[1],"is":[2],"called":[3],"solid":[4,27,54,81],"if,":[5],"roughly":[6],"speaking,":[7],"any":[8],"correctly-transmitted":[9],"codeword":[10],"in":[11,29,34],"an":[12,70],"arbitrarily":[13],"corrupted":[14],"string":[15],"of":[16,52,74,78,92],"codewords":[17,31],"can":[18],"still":[19],"be":[20,61],"decoded":[21],"correctly":[22],"and":[23,83],"unambiguously.":[24],"So-called":[25],"variable-length":[26,53,80],"codes,":[28,82],"which":[30],"may":[32,60],"differ":[33],"length,":[35],"have":[36],"been":[37],"studied":[38],"by":[39],"various":[40],"authors.":[41],"In":[42],"this":[43],"short":[44],"note,":[45],"we":[46],"observe":[47],"that":[48],"a":[49,75,85,89],"recent":[50],"construction":[51],"codes":[55,59],"based":[56],"on":[57],"binary":[58,93],"extended":[62],"to":[63,88],"arbitrary":[64],"n-ary":[65],"codes.":[66],"We":[67],"further":[68],"prove":[69],"interesting":[71],"error-detection":[72],"property":[73],"specific":[76],"subfamily":[77],"these":[79],"give":[84],"concrete":[86],"application":[87],"certain":[90],"type":[91],"code.":[94]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-03-25T00:00:00"}
