{"id":"https://openalex.org/W4411049584","doi":"https://doi.org/10.3934/amc.2025024","title":"Full flag codes are the &lt;inline-formula&gt;&lt;tex-math id=\"M1\"&gt;$ q $&lt;/tex-math&gt;&lt;/inline-formula&gt;-analog of permutation codes with the Manhattan metric","display_name":"Full flag codes are the &lt;inline-formula&gt;&lt;tex-math id=\"M1\"&gt;$ q $&lt;/tex-math&gt;&lt;/inline-formula&gt;-analog of permutation codes with the Manhattan metric","publication_year":2025,"publication_date":"2025-06-05","ids":{"openalex":"https://openalex.org/W4411049584","doi":"https://doi.org/10.3934/amc.2025024"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2025024","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025024","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416cf1b924fa00d9d4128d","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416cf1b924fa00d9d4128d","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079433304","display_name":"Michael Braun","orcid":"https://orcid.org/0000-0001-9816-2216"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Braun","raw_affiliation_strings":["University of Applied Sciences Darmstadt , Faculty of Computer Science , Germany"],"affiliations":[{"raw_affiliation_string":"University of Applied Sciences Darmstadt , Faculty of Computer Science , Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079433304"],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06545558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"0","first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9990000128746033,"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/mathematics","display_name":"Mathematics","score":0.8725354671478271},{"id":"https://openalex.org/keywords/flag","display_name":"Flag (linear algebra)","score":0.6402095556259155},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6062846779823303},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4585781395435333},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.45582282543182373},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4188898205757141},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3929775059223175},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.18971127271652222},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12607252597808838},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.03434896469116211}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8725354671478271},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.6402095556259155},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6062846779823303},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4585781395435333},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.45582282543182373},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4188898205757141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3929775059223175},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.18971127271652222},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12607252597808838},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.03434896469116211},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2025024","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025024","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416cf1b924fa00d9d4128d","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2025024","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025024","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416cf1b924fa00d9d4128d","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411049584.pdf","grobid_xml":"https://content.openalex.org/works/W4411049584.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1672384623","https://openalex.org/W1971599520","https://openalex.org/W2086724086","https://openalex.org/W2139416652","https://openalex.org/W2545908865","https://openalex.org/W2608395580","https://openalex.org/W2792356213","https://openalex.org/W2988678468","https://openalex.org/W3091366941","https://openalex.org/W3099741249","https://openalex.org/W3112433699","https://openalex.org/W3207061113","https://openalex.org/W3216953947","https://openalex.org/W4205617790"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2324035390","https://openalex.org/W2963151310","https://openalex.org/W3175137310","https://openalex.org/W2583526987","https://openalex.org/W3034984450","https://openalex.org/W2695311495","https://openalex.org/W3139271019","https://openalex.org/W2098156551","https://openalex.org/W4401592300"],"abstract_inverted_index":{"In":[0,82],"this":[1,55],"article":[2],"we":[3,27,117],"prove":[4,53],"that":[5,54,119],"full":[6,86,134],"flag":[7,120],"codes":[8,16,98,121,146],"are":[9,125],"the":[10,19,23,29,63,70,79,102,127,140],"$":[11,31,33,39,41,47,49,66,68,73,76,91,95,128,141],"q":[12,129,142],"$-analog":[13,130,143],"of":[14,34,37,42,45,65,85,88,131,133,136,144],"permutation":[15,97,145],"equipped":[17,77,147],"with":[18,78,99,148],"Manhattan":[20,80,103,149],"metric":[21,59,71,150],"by":[22,108,111,115],"following":[24],"approach:":[25],"First,":[26],"consider":[28],"set":[30,51,56],"\\text{Ch}(P(n),t)":[32,67],"finite":[35],"chains":[36,87,135],"length":[38],"t":[40,92],"nested":[43],"subsets":[44,89,110,137],"an":[46],"n":[48],"element":[50],"and":[52,113,138],"forms":[57],"a":[58,106],"space.":[60],"We":[61],"show":[62],"connection":[64],"to":[69,101],"space":[72],"{\\mathbb":[74],"Z}_{t+1}^n":[75],"distance.":[81,104],"particular,":[83],"sets":[84,132],"for":[90,122],"=":[93],"n-1":[94],"form":[96],"respect":[100],"As":[105],"consequence,":[107],"replacing":[109],"subspaces":[112],"cardinalities":[114],"dimensions":[116],"obtain":[118],"network":[123],"coding":[124],"obviously":[126],"hence":[139],"as":[151],"well.":[152]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
