{"id":"https://openalex.org/W2043608224","doi":"https://doi.org/10.1137/s0895480102416192","title":"Codes Closed under Arbitrary Abelian Group of Permutations","display_name":"Codes Closed under Arbitrary Abelian Group of Permutations","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2043608224","doi":"https://doi.org/10.1137/s0895480102416192","mag":"2043608224"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480102416192","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480102416192","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064926409","display_name":"Bikash Kumar Dey","orcid":"https://orcid.org/0000-0003-0333-2257"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bikash Kumar Dey","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015398340","display_name":"B. Sundar Rajan","orcid":"https://orcid.org/0000-0002-7847-0200"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Sundar Rajan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064926409"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9251,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.81372877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"1","first_page":"1","last_page":"18"},"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/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":1.0,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9968000054359436,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.994700014591217,"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/abelian-group","display_name":"Abelian group","score":0.8137945532798767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7589017152786255},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.6831321716308594},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5515159368515015},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.5477744936943054},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5235616564750671},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5157968997955322},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5109257102012634},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5038034319877625},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.29317617416381836},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14446207880973816}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8137945532798767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7589017152786255},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.6831321716308594},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5515159368515015},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.5477744936943054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5235616564750671},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5157968997955322},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5109257102012634},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5038034319877625},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.29317617416381836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14446207880973816},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0895480102416192","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480102416192","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.iisc.ac.in:2310","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196309","display_name":"NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.508.5936","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.508.5936","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.iisc.ernet.in/8964/1/Codes_Closed.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1503864546","https://openalex.org/W1581232847","https://openalex.org/W1617868970","https://openalex.org/W1975875771","https://openalex.org/W2014783995","https://openalex.org/W2062642782","https://openalex.org/W2065026674","https://openalex.org/W2075451506","https://openalex.org/W2089921613","https://openalex.org/W2099727759","https://openalex.org/W2131418871","https://openalex.org/W2148759836","https://openalex.org/W2160996071","https://openalex.org/W2809309076","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2059476306","https://openalex.org/W1615633844","https://openalex.org/W2115706646","https://openalex.org/W2145201720","https://openalex.org/W2255054582","https://openalex.org/W4376312529","https://openalex.org/W2095450438","https://openalex.org/W2171478552","https://openalex.org/W2112748907","https://openalex.org/W2159680542"],"abstract_inverted_index":{"Algebraic":[0],"structure":[1,37],"of":[2,12,38,58,69,86,90,112,149,160,177],"codes":[3,47,57,60,64,72,89,174],"over":[4,93,116],"Fq,":[5],"closed":[6],"under":[7],"arbitrary":[8],"abelian":[9,41,75],"group":[10,76],"G":[11,51,77],"permutations":[13],"with":[14,48,145,175],"exponent":[15],"relatively":[16],"prime":[17],"to":[18,52,127,157,170],"q,":[19],"called":[20],"G-invariant":[21,59,63,70,135],"codes,":[22,40,42,44],"is":[23,78,155],"investigated":[24],"using":[25],"a":[26,103,110,129,134,141,146],"transform":[27],"domain":[28],"approach.":[29],"In":[30,80,164],"particular,":[31,81,165],"this":[32,82,166],"general":[33],"approach":[34,100],"unveils":[35],"algebraic":[36],"quasi-cyclic":[39,143,173],"cyclic":[43],"and":[45,61,120],"quasi-abelian":[46,162],"restriction":[49],"on":[50,105],"appropriate":[53],"special":[54],"cases.":[55],"Dual":[56],"self-dual":[62,71,87],"are":[65],"characterized.":[66],"The":[67],"number":[68,85],"for":[73,101,133,140],"any":[74],"found.":[79],"gives":[83],"the":[84,106,152,158,181],"l-quasi-cyclic":[88],"length":[91],"ml":[92],"Fq":[94],"when":[95],"(m,q)=1.":[96],"We":[97],"extend":[98],"Tanner's":[99],"getting":[102],"bound":[104,132],"minimum":[107,130],"distance":[108,131],"from":[109],"set":[111],"parity":[113,178],"check":[114],"equations":[115],"an":[117],"extension":[118],"field":[119],"outline":[121],"how":[122],"it":[123],"can":[124,167],"be":[125,168],"used":[126,169],"get":[128],"code.":[136],"Karlin's":[137],"decoding":[138],"algorithm":[139],"systematic":[142,161,172],"code":[144],"single":[147],"row":[148],"circulants":[150,179],"in":[151,180],"generator":[153,182],"matrix":[154],"extended":[156],"case":[159],"codes.":[163],"decode":[171],"columns":[176],"matrix.":[183]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}