{"id":"https://openalex.org/W4401749640","doi":"https://doi.org/10.1109/tit.2024.3448230","title":"Improving Explicit Constructions of <i>r</i>-PD-Sets for <i>Z\u209as</i>-Linear Generalized Hadamard Codes","display_name":"Improving Explicit Constructions of <i>r</i>-PD-Sets for <i>Z\u209as</i>-Linear Generalized Hadamard Codes","publication_year":2024,"publication_date":"2024-08-22","ids":{"openalex":"https://openalex.org/W4401749640","doi":"https://doi.org/10.1109/tit.2024.3448230"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3448230","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/tit.2024.3448230","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"http://dx.doi.org/10.1109/tit.2024.3448230","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082545070","display_name":"Josep Rif\u00e0","orcid":"https://orcid.org/0000-0001-9199-4001"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josep Rif\u00e0","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9199-4001","affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Barcelona, Spain","institution_ids":[]}]},{"author_position":"middle","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":"Adri\u00e1n Torres-Mart\u00edn","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Barcelona, 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, Barcelona, 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":"Merc\u00e8 Villanueva","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut&#x00F2;noma de Barcelona, Barcelona, 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, Barcelona, Spain","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10445672,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"12","first_page":"8675","last_page":"8687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9993000030517578,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9993000030517578,"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/T11873","display_name":"PAPR reduction in OFDM","score":0.9936000108718872,"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/T10575","display_name":"Wireless Communication Networks Research","score":0.989799976348877,"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/hadamard-transform","display_name":"Hadamard transform","score":0.7417700886726379},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5606945753097534},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5065544843673706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4594901204109192},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.413131445646286},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.32670721411705017},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.30164122581481934},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.264759361743927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08823433518409729}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.7417700886726379},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5606945753097534},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5065544843673706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4594901204109192},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.413131445646286},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.32670721411705017},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.30164122581481934},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.264759361743927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08823433518409729}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2024.3448230","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/tit.2024.3448230","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:ddd.uab.cat:302357","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/302357","pdf_url":"https://ddd.uab.cat/pub/artpub/2024/302357/ieetrainf_a2024m12v70n12p8675-8687.pdf","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"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":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1109/tit.2024.3448230","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/tit.2024.3448230","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1643949827","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2352338862","display_name":null,"funder_award_id":"2021 SGR 00643","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G2855141111","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"},{"id":"https://openalex.org/G288263039","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4882408770","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5772968582","display_name":null,"funder_award_id":"PID2022-137924NB-I00 (AEI/10.13039/501100011033)","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G5852091828","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7535663061","display_name":null,"funder_award_id":"AEI/10.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320326262","display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a","ror":"https://ror.org/03sv46s19"},{"id":"https://openalex.org/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W597381772","https://openalex.org/W1503013413","https://openalex.org/W1597948074","https://openalex.org/W1604526698","https://openalex.org/W1640881979","https://openalex.org/W1972368298","https://openalex.org/W1987121126","https://openalex.org/W2010238614","https://openalex.org/W2010825458","https://openalex.org/W2038681062","https://openalex.org/W2039133144","https://openalex.org/W2063301472","https://openalex.org/W2069145139","https://openalex.org/W2070442620","https://openalex.org/W2081939650","https://openalex.org/W2103398070","https://openalex.org/W2109887866","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/W3101163237","https://openalex.org/W3103130602","https://openalex.org/W3106364761","https://openalex.org/W3134411742","https://openalex.org/W3201287454","https://openalex.org/W4214810519","https://openalex.org/W4225530725","https://openalex.org/W4285145726","https://openalex.org/W4285215921","https://openalex.org/W4286484304","https://openalex.org/W4300529123","https://openalex.org/W4312056005","https://openalex.org/W4386869659","https://openalex.org/W4387835508","https://openalex.org/W4388795554"],"related_works":["https://openalex.org/W135568846","https://openalex.org/W2460434904","https://openalex.org/W1789159349","https://openalex.org/W2113911300","https://openalex.org/W2151857680","https://openalex.org/W832867880","https://openalex.org/W2147254059","https://openalex.org/W4386066307","https://openalex.org/W917159298","https://openalex.org/W1975697476"],"abstract_inverted_index":{"It":[0],"is":[1],"known":[2,169],"that":[3],"<inline-formula":[4,19,30,48,87,94,106,130,142],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,20,31,49,88,95,107,131,143],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[6,21,32,50,89,96,108,132,144],"<tex-math":[7,22,33,51,90,97,109,133,145],"notation=\"LaTeX\">$\\mathbb":[8,23,34,52,98],"{Z}_{p^{s}}$":[9,24,35,53,99],"</tex-math></inline-formula>-linear":[10,54,100],"codes,":[11,121],"which":[12,69,136],"are":[13,37,70,114,137],"the":[14,59,65,73,78,163],"Gray":[15],"map":[16],"image":[17],"of":[18,67,72,77,82,84,104,126,128,159],"</tex-math></inline-formula>-additive":[25],"codes":[26,28,55,103],"(linear":[27],"over":[29],"</tex-math></inline-formula>),":[36],"systematic":[38,41],"and":[39],"a":[40],"encoding":[42],"has":[43],"been":[44],"found.":[45],"This":[46],"makes":[47],"suitable":[56,138],"to":[57,153,162],"apply":[58],"permutation":[60,74],"decoding":[61],"method,":[62],"based":[63],"on":[64],"existence":[66],"r-PD-sets,":[68],"subsets":[71],"automorphism":[75],"group":[76],"code.":[79],"Some":[80],"constructions":[81,125],"r-PD-sets":[83,127,156],"minimum":[85],"size":[86,129],"notation=\"LaTeX\">$r+1$":[91,134],"</tex-math></inline-formula>":[92,113],"for":[93,119,139,157],"generalized":[101],"Hadamard":[102],"type":[105],"notation=\"LaTeX\">$(n;t_{1},":[110],"{\\dots":[111,147],"},t_{s})$":[112],"known.":[115],"In":[116],"this":[117],"paper,":[118],"these":[120],"we":[122],"present":[123],"new":[124,155],"</tex-math></inline-formula>,":[135],"all":[140],"parameters":[141],"notation=\"LaTeX\">$t_{1},":[146],"},t_{s}$":[148],"</tex-math></inline-formula>.":[149],"These":[150],"allow":[151],"us":[152],"obtain":[154],"values":[158],"r":[160],"closer":[161],"theoretical":[164],"upper":[165],"bound,":[166],"improving":[167],"previous":[168],"results.":[170]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2024-08-23T00:00:00"}