{"id":"https://openalex.org/W4417156383","doi":"https://doi.org/10.3390/e27121245","title":"On Best Erasure Wiretap Codes: Equivocation Matrices and Design Principles","display_name":"On Best Erasure Wiretap Codes: Equivocation Matrices and Design Principles","publication_year":2025,"publication_date":"2025-12-09","ids":{"openalex":"https://openalex.org/W4417156383","doi":"https://doi.org/10.3390/e27121245","pmid":"https://pubmed.ncbi.nlm.nih.gov/41440447"},"language":"en","primary_location":{"id":"doi:10.3390/e27121245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27121245","pdf_url":"https://www.mdpi.com/1099-4300/27/12/1245/pdf?version=1765283915","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/12/1245/pdf?version=1765283915","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042317703","display_name":"Willie K. Harrison","orcid":"https://orcid.org/0000-0002-9375-9440"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Willie K. Harrison","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"],"raw_orcid":"https://orcid.org/0000-0002-9375-9440","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA","institution_ids":["https://openalex.org/I100005738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120731428","display_name":"Truman Welling","orcid":null},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Truman Welling","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA","institution_ids":["https://openalex.org/I100005738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105658113","display_name":"Andrew Swain","orcid":"https://orcid.org/0009-0000-0471-5407"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Swain","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"],"raw_orcid":"https://orcid.org/0009-0000-0471-5407","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA","institution_ids":["https://openalex.org/I100005738"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049419980","display_name":"Morteza Shoushtari","orcid":"https://orcid.org/0000-0002-4152-0163"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Morteza Shoushtari","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA","institution_ids":["https://openalex.org/I100005738"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042317703"],"corresponding_institution_ids":["https://openalex.org/I100005738"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.232911,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"12","first_page":"1245","last_page":"1245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.6389999985694885,"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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.6389999985694885,"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/T11130","display_name":"Coding theory and cryptography","score":0.08550000190734863,"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":0.05590000003576279,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/equivocation","display_name":"Equivocation","score":0.7519999742507935},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.5812000036239624},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5091000199317932},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.46320000290870667},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.4620000123977661},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.4293000102043152},{"id":"https://openalex.org/keywords/information-theoretic-security","display_name":"Information-theoretic security","score":0.4172999858856201},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.38909998536109924},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.3878999948501587}],"concepts":[{"id":"https://openalex.org/C17859611","wikidata":"https://www.wikidata.org/wiki/Q10797615","display_name":"Equivocation","level":2,"score":0.7519999742507935},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6534000039100647},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.5812000036239624},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5091000199317932},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5008000135421753},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.4620000123977661},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4293000102043152},{"id":"https://openalex.org/C47191418","wikidata":"https://www.wikidata.org/wiki/Q3510462","display_name":"Information-theoretic security","level":3,"score":0.4172999858856201},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.367900013923645},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.3617999851703644},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.335999995470047},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.32190001010894775},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3034999966621399},{"id":"https://openalex.org/C178005623","wikidata":"https://www.wikidata.org/wiki/Q308859","display_name":"Anonymity","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2824999988079071},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.2791999876499176},{"id":"https://openalex.org/C202932441","wikidata":"https://www.wikidata.org/wiki/Q55611017","display_name":"Forward error correction","level":3,"score":0.2775999903678894},{"id":"https://openalex.org/C95713431","wikidata":"https://www.wikidata.org/wiki/Q631425","display_name":"Vulnerability (computing)","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.25679999589920044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2540999948978424},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2517000138759613},{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.25119999051094055},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27121245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27121245","pdf_url":"https://www.mdpi.com/1099-4300/27/12/1245/pdf?version=1765283915","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41440447","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41440447","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:9eed8122dba3407088bde0b9b697550d","is_oa":true,"landing_page_url":"https://doaj.org/article/9eed8122dba3407088bde0b9b697550d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 12, p 1245 (2025)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12731369","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12731369/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27121245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27121245","pdf_url":"https://www.mdpi.com/1099-4300/27/12/1245/pdf?version=1765283915","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4505975952","display_name":"CIF: Small: Best Wiretap Codes for Real-world Physical-layer Security","funder_award_id":"1910812","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417156383.pdf","grobid_xml":"https://content.openalex.org/works/W4417156383.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W949353694","https://openalex.org/W1536930200","https://openalex.org/W1544547601","https://openalex.org/W1553965766","https://openalex.org/W1562070166","https://openalex.org/W1565176535","https://openalex.org/W1957358593","https://openalex.org/W2029720112","https://openalex.org/W2043769961","https://openalex.org/W2044126357","https://openalex.org/W2056327536","https://openalex.org/W2062612962","https://openalex.org/W2068887604","https://openalex.org/W2078577886","https://openalex.org/W2097117337","https://openalex.org/W2108723203","https://openalex.org/W2109394932","https://openalex.org/W2120869110","https://openalex.org/W2124602541","https://openalex.org/W2127558904","https://openalex.org/W2140730398","https://openalex.org/W2144007657","https://openalex.org/W2156186849","https://openalex.org/W2262889796","https://openalex.org/W2582151064","https://openalex.org/W2610964475","https://openalex.org/W2887092854","https://openalex.org/W2912183452","https://openalex.org/W2914714618","https://openalex.org/W2963414437","https://openalex.org/W2964475833","https://openalex.org/W2976127079","https://openalex.org/W2977099835","https://openalex.org/W3041293626","https://openalex.org/W3081299694","https://openalex.org/W3216271775","https://openalex.org/W4234572373","https://openalex.org/W4387185648","https://openalex.org/W4403752276","https://openalex.org/W4415366823"],"related_works":[],"abstract_inverted_index":{"Physical-layer":[0],"security":[1],"can":[2],"aid":[3],"in":[4,49,71,98,135],"establishing":[5],"secure":[6,40],"telecommunication":[7],"networks":[8],"including":[9],"cellular,":[10],"Internet":[11],"of":[12,84],"Things,":[13],"and":[14,65,69,74,90],"telemetry":[15,23],"networks,":[16],"among":[17],"others.":[18],"Channel":[19],"sounding":[20],"techniques":[21],"and/or":[22],"systems":[24],"for":[25,55,86,101,116],"reporting":[26],"channel":[27],"conditions,":[28],"coupled":[29],"with":[30],"superior":[31],"wiretap":[32,51,59,78,87],"code":[33,53,118],"design":[34,54],"are":[35,126],"necessary":[36],"to":[37,93],"implement":[38],"such":[39],"systems.":[41],"In":[42],"this":[43],"paper,":[44],"we":[45,107],"present":[46],"recent":[47],"results":[48],"best":[50,102,111],"coset":[52,88],"the":[56,76,82,95,110],"binary":[57],"erasure":[58],"channel.":[60],"We":[61,80,120],"define":[62],"equivocation":[63],"matrices,":[64],"showcase":[66],"their":[67,136],"properties":[68],"utility":[70],"constructing":[72],"good,":[73],"even":[75],"best,":[77],"codes.":[79,104],"outline":[81],"notion":[83],"equivalence":[85],"codes,":[89],"use":[91],"it":[92],"reduce":[94],"search":[96],"space":[97],"exhaustive":[99],"searches":[100],"small":[103],"Through":[105],"example,":[106],"show":[108],"that":[109,123],"codes":[112,125,129],"do":[113],"not":[114],"exist":[115],"some":[117],"sizes.":[119],"also":[121],"prove":[122],"simplex":[124],"better":[127],"than":[128],"repeating":[130],"one":[131],"column":[132],"multiple":[133],"times":[134],"generator":[137],"matrix.":[138]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-12-09T00:00:00"}
