{"id":"https://openalex.org/W4214810519","doi":"https://doi.org/10.1109/tit.2022.3157192","title":"Systematic Encoding and Permutation Decoding for Z<sub>p<sup>s</sup></sub>-Linear Codes","display_name":"Systematic Encoding and Permutation Decoding for Z<sub>p<sup>s</sup></sub>-Linear Codes","publication_year":2022,"publication_date":"2022-03-04","ids":{"openalex":"https://openalex.org/W4214810519","doi":"https://doi.org/10.1109/tit.2022.3157192"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3157192","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3157192","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5083305829","display_name":"Adri\u00e1n Torres-Mart\u00edn","orcid":"https://orcid.org/0000-0002-2489-8930"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adrian Torres-Martin","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Cerdanyola del Vall&#x00E8;s, Spain"],"raw_orcid":"https://orcid.org/0000-0002-2489-8930","affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Cerdanyola del Vall&#x00E8;s, Spain","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080668151","display_name":"Merc\u00e8 Villanueva","orcid":"https://orcid.org/0000-0001-6179-0833"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Merce Villanueva","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Cerdanyola del Vall&#x00E8;s, Spain"],"raw_orcid":"https://orcid.org/0000-0001-6179-0833","affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Cerdanyola del Vall&#x00E8;s, Spain","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2486,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8246292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"68","issue":"7","first_page":"4435","last_page":"4443"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9962999820709229,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9958999752998352,"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/notation","display_name":"Notation","score":0.6063429713249207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45700135827064514},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4546809494495392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3918226659297943},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3791116774082184},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23719453811645508},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.19067218899726868},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10876467823982239}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6063429713249207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45700135827064514},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4546809494495392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3918226659297943},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3791116774082184},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23719453811645508},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.19067218899726868},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10876467823982239},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3157192","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3157192","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6732827572","display_name":null,"funder_award_id":"PID2019-104664GB-I00 (AEI/10.13039/501100011033)","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1503013413","https://openalex.org/W1516318957","https://openalex.org/W1597948074","https://openalex.org/W1606480398","https://openalex.org/W1964495070","https://openalex.org/W1972368298","https://openalex.org/W1987121126","https://openalex.org/W2010238614","https://openalex.org/W2010825458","https://openalex.org/W2038681062","https://openalex.org/W2062142782","https://openalex.org/W2063301472","https://openalex.org/W2070442620","https://openalex.org/W2103398070","https://openalex.org/W2109887866","https://openalex.org/W2172400893","https://openalex.org/W2395800580","https://openalex.org/W2739214207","https://openalex.org/W2889940767","https://openalex.org/W2892003982","https://openalex.org/W2907006411","https://openalex.org/W2962972548","https://openalex.org/W2990636281","https://openalex.org/W2991239327","https://openalex.org/W3103130602","https://openalex.org/W3106364761","https://openalex.org/W3145360821","https://openalex.org/W3201287454","https://openalex.org/W4225530725","https://openalex.org/W4285215921","https://openalex.org/W6630182224"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Linear":[0],"codes":[1,30,42,52],"over":[2,53,83,202],"<inline-formula":[3,12,21,34,54,62,71,84,104,121,166,176,184,203],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,13,22,35,55,63,72,85,105,122,167,177,185,204],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[5,14,23,36,56,64,73,86,106,123,168,178,186,205],"<tex-math":[6,15,24,37,57,65,74,87,107,124,169,179,187,206],"notation=\"LaTeX\">$\\mathbb":[7,25,38,58,66,75,88,108,125,170,207],"{Z}_{p^{s}}$":[8,39,76,109,171],"</tex-math></inline-formula>":[9,17,27,40,60,68,77,90,110,127,172,182,189,209],"of":[10,20,50,102,218],"length":[11],"notation=\"LaTeX\">$n$":[16],"are":[18,31],"subgroups":[19],"{Z}_{p^{s}}^{n}$":[26],".":[28,69],"These":[29],"also":[32,192],"called":[33],"-additive":[41,111],"and":[43,61,183,214],"can":[44],"be":[45],"seen":[46],"as":[47],"a":[48,81,103,115,147,161,194],"generalization":[49],"linear":[51],"{Z}_{2}$":[59],"{Z}_{4}$":[67,126],"A":[70],"-linear":[78,128,173],"code":[79,82,142,174,201],"is":[80,96,137],"{Z}_{p}$":[89,208],",":[91,210],"not":[92,211],"necessarily":[93,144,212],"linear,":[94,213],"which":[95,136],"the":[97],"generalized":[98],"Gray":[99],"map":[100],"image":[101],"code.":[112],"In":[113,152],"2015,":[114],"systematic":[116,148,162,200,223],"encoding":[117,163,224],"was":[118,150],"found":[119],"for":[120,139,164,198],"codes.":[129],"Moreover,":[130],"an":[131],"alternative":[132],"permutation":[133,195],"decoding":[134,196,227],"method,":[135],"suitable":[138],"any":[140,165,199],"binary":[141],"(not":[143],"linear)":[145],"with":[146,175],"encoding,":[149],"established.":[151],"this":[153,222,226],"paper,":[154],"we":[155],"generalize":[156],"these":[157],"results":[158],"by":[159],"presenting":[160],"notation=\"LaTeX\">$s\\geq":[180],"2$":[181],"notation=\"LaTeX\">$p$":[188],"prime.":[190],"We":[191],"describe":[193],"method":[197],"show":[215],"some":[216],"examples":[217],"how":[219],"to":[220],"use":[221],"in":[225],"method.":[228]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}