{"id":"https://openalex.org/W4311839832","doi":"https://doi.org/10.1109/itw54588.2022.9965801","title":"On the Classification of \u2124<sub>p</sub>\u2124<sub>p</sub><sup>2</sup>-Linear Generalized Hadamard Codes","display_name":"On the Classification of \u2124<sub>p</sub>\u2124<sub>p</sub><sup>2</sup>-Linear Generalized Hadamard Codes","publication_year":2022,"publication_date":"2022-11-01","ids":{"openalex":"https://openalex.org/W4311839832","doi":"https://doi.org/10.1109/itw54588.2022.9965801"},"language":"en","primary_location":{"id":"doi:10.1109/itw54588.2022.9965801","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw54588.2022.9965801","pdf_url":null,"source":{"id":"https://openalex.org/S4363606450","display_name":"2022 IEEE Information Theory Workshop (ITW)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-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/A5011940850","display_name":"Dipak K. Bhunia","orcid":"https://orcid.org/0000-0003-4852-8739"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dipak Kumar Bhunia","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Dept. of Inf. and Communications Engineering,Barcelona,Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Dept. of Inf. and Communications Engineering,Barcelona,Spain","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065292754","display_name":"Cristina Fern\u00e1ndez-C\u00f3rdoba","orcid":"https://orcid.org/0000-0001-5880-144X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cristina Fernandez-Cordoba","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Dept. of Inf. and Com. Engineering,Barcelona,Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Dept. of Inf. and Com. Engineering,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":"Merce Villanueva","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Dept. of Inf. and Com. Engineering,Barcelona,Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Dept. of Inf. and Com. Engineering,Barcelona,Spain","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011940850"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2079,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42970265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9991999864578247,"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":0.9940999746322632,"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/combinatorics","display_name":"Combinatorics","score":0.5454060435295105},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.422943115234375},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.41323620080947876},{"id":"https://openalex.org/keywords/stereochemistry","display_name":"Stereochemistry","score":0.36930930614471436},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.36305123567581177},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32830750942230225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22838884592056274},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15267598628997803},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09053713083267212}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5454060435295105},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.422943115234375},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.41323620080947876},{"id":"https://openalex.org/C71240020","wikidata":"https://www.wikidata.org/wiki/Q186011","display_name":"Stereochemistry","level":1,"score":0.36930930614471436},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36305123567581177},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32830750942230225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22838884592056274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15267598628997803},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09053713083267212},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itw54588.2022.9965801","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw54588.2022.9965801","pdf_url":null,"source":{"id":"https://openalex.org/S4363606450","display_name":"2022 IEEE Information Theory Workshop (ITW)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"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":28,"referenced_works":["https://openalex.org/W1597948074","https://openalex.org/W1640881979","https://openalex.org/W1972368298","https://openalex.org/W1981315250","https://openalex.org/W1987121126","https://openalex.org/W2019915930","https://openalex.org/W2038681062","https://openalex.org/W2062692517","https://openalex.org/W2064737342","https://openalex.org/W2080516816","https://openalex.org/W2081939650","https://openalex.org/W2109887866","https://openalex.org/W2124691561","https://openalex.org/W2172400893","https://openalex.org/W2395800580","https://openalex.org/W2739214207","https://openalex.org/W2889940767","https://openalex.org/W2892003982","https://openalex.org/W2991239327","https://openalex.org/W3101163237","https://openalex.org/W3103130602","https://openalex.org/W3106364761","https://openalex.org/W3201287454","https://openalex.org/W4211147273","https://openalex.org/W4225530725","https://openalex.org/W4286484304","https://openalex.org/W4300529123","https://openalex.org/W6630182224"],"related_works":["https://openalex.org/W1982241170","https://openalex.org/W2116282083","https://openalex.org/W2386549147","https://openalex.org/W1978051046","https://openalex.org/W2012411066","https://openalex.org/W2950361249","https://openalex.org/W117514602","https://openalex.org/W1553886475","https://openalex.org/W1534096932","https://openalex.org/W1901293447"],"abstract_inverted_index":{"The":[0],"${\\mathbb{Z}_p}{\\mathbb{Z}_{{p^2}}}{\\text{":[1,40,129,154,184],"-":[2,14,41,130,155,166,172,185],"additive}}$":[3,42],"codes":[4,44,89,108,133,176,189],"are":[5,90,177],"subgroups":[6],"of":[7,32,39,45,128,150,153,183],"$\\mathbb{Z}_p^{{\\alpha":[8],"_1}}":[9],"\\times":[10],"\\mathbb{Z}_{{p^2}}^{{\\alpha":[11],"_2}}$.":[12],"A${\\mathbb{Z}_p}{\\mathbb{Z}_{{p^2}}}{\\text{":[13],"linear}}$":[15,131,167],"generalized":[16],"Hadamard":[17,168],"(GH)":[18],"code":[19,23],"is":[20,27,79,94],"a":[21,33],"GH":[22,43,88,107,132,158,175,188],"over":[24,92],"${\\mathbb{Z}_p}$":[25,93],"which":[26,83],"the":[28,85,135,148,170,181],"Gray":[29],"map":[30],"image":[31],"${\\mathbb{Z}_p}{\\mathbb{Z}_{{p^2}}}$-additive":[34],"code.":[35],"A":[36],"recursive":[37,126],"construction":[38],"type":[46],"(\u03b1":[47],"<inf":[48,53,58,63,69,74],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[49,54,59,64,70,75],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</inf>":[50,60,71],",":[51,61,72],"\u03b1":[52],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>":[55,65,76],";":[56],"t":[57,62,68,73],")":[66],"with":[67,109,190],"\u2265":[77,197],"1":[78],"known,":[80],"and":[81,138],"for":[82,105],"types":[84],"corresponding":[86],"${\\mathbb{Z}_p}{\\mathbb{Z}_{{p^2}}}$-linear":[87,106],"nonlinear":[91],"also":[95],"known.":[96],"In":[97],"this":[98],"paper,":[99],"we":[100,123,141,146,161],"generalize":[101],"some":[102,151],"known":[103],"results":[104],"p":[110,196],"=":[111],"2":[112],"to":[113],"any":[114],"p\u22653":[115],"prime":[116],"when":[117,195],"${\\alpha":[118,191],"_1}":[119,192],"\\ne":[120,193],"0$.":[121],"First,":[122],"present":[124],"new":[125],"constructions":[127],"having":[134],"same":[136],"type,":[137],"show":[139,162],"that":[140],"obtained":[142],"equivalent":[143],"codes.":[144,159],"Then,":[145],"compute":[147],"rank":[149],"families":[152],"Linear":[156,173,186],"}}$":[157,174,187],"Finally,":[160],"that,":[163],"unlike":[164],"${\\mathbb{Z}_4}{\\text{":[165],"codes,":[169],"${\\mathbb{Z}_{{p^2}}}{\\text{":[171],"not":[178],"included":[179],"in":[180],"family":[182],"0$":[194],"3":[198],"prime.":[199]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}