{"id":"https://openalex.org/W4386066056","doi":"https://doi.org/10.1109/isit54713.2023.10206645","title":"On \u2124 <sub>2</sub> \u2124 <sub>4</sub> \u2124 <sub>8</sub> -Additive Hadamard Codes","display_name":"On \u2124 <sub>2</sub> \u2124 <sub>4</sub> \u2124 <sub>8</sub> -Additive Hadamard Codes","publication_year":2023,"publication_date":"2023-06-25","ids":{"openalex":"https://openalex.org/W4386066056","doi":"https://doi.org/10.1109/isit54713.2023.10206645"},"language":"en","primary_location":{"id":"doi:10.1109/isit54713.2023.10206645","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206645","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"conference-paper","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":false,"raw_author_name":"Dipak Kumar Bhunia","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Department of Information and Communications Engineering,Cerdanyola del Vall&#x00E8;s,Spain,08193"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Department of Information and Communications Engineering,Cerdanyola del Vall&#x00E8;s,Spain,08193","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 Fern\u00e1ndez-C\u00f3rdoba","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Department of Information and Communications Engineering,Cerdanyola del Vall&#x00E8;s,Spain,08193"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Department of Information and Communications Engineering,Cerdanyola del Vall&#x00E8;s,Spain,08193","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":["Universitat Aut&#x00F2;noma de Barcelona,Department of Information and Communications Engineering,Cerdanyola del Vall&#x00E8;s,Spain,08193"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Department of Information and Communications Engineering,Cerdanyola del Vall&#x00E8;s,Spain,08193","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6534,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68385006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"276","last_page":"281"},"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":0.9995999932289124,"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/T10849","display_name":"Finite Group Theory Research","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5074965357780457},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3583225905895233},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28589776158332825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1875740885734558},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05703777074813843}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5074965357780457},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3583225905895233},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28589776158332825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1875740885734558},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05703777074813843}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit54713.2023.10206645","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206645","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","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":26,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1640881979","https://openalex.org/W1981315250","https://openalex.org/W1987121126","https://openalex.org/W2010238614","https://openalex.org/W2038681062","https://openalex.org/W2064737342","https://openalex.org/W2081939650","https://openalex.org/W2109887866","https://openalex.org/W2124691561","https://openalex.org/W2172400893","https://openalex.org/W2395800580","https://openalex.org/W2576389538","https://openalex.org/W2889940767","https://openalex.org/W2892003982","https://openalex.org/W2990636281","https://openalex.org/W2991239327","https://openalex.org/W3101163237","https://openalex.org/W3106364761","https://openalex.org/W4225530725","https://openalex.org/W4285145726","https://openalex.org/W4286484304","https://openalex.org/W4300529123","https://openalex.org/W4311839832","https://openalex.org/W4312056005","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/W2051487156","https://openalex.org/W1553886475","https://openalex.org/W2073681303"],"abstract_inverted_index":{"The":[0],"\u21242\u21244\u21248-additive":[1,30,69],"codes":[2,43,47,71,100,120,146],"are":[3,101,147],"subgroups":[4],"of":[5,28,68,72,117,126],"$\\mathbb{Z}_2^{{\\alpha":[6],"_1}}":[7],"\\times":[8,11],"\\mathbb{Z}_4^{{\\alpha":[9],"_2}}":[10],"\\mathbb{Z}_8^{{\\alpha":[12],"_3}}$.":[13],"A":[14],"\u21242\u21244\u21248-linear":[15,45,98,118,144],"Hadamard":[16,20,42,46,70,99,111,119,130,145,164],"code":[17,21],"is":[18,23],"a":[19,29,65],"which":[22,94],"the":[24,96,124,141],"Gray":[25],"map":[26],"image":[27],"code.":[31],"In":[32],"this":[33,115],"paper,":[34],"we":[35,63,91,106,133],"generalize":[36],"some":[37],"known":[38],"results":[39],"for":[40,93,136,138],"${\\mathbb{Z}_2}{\\mathbb{Z}_4}$-linear":[41,110,156],"to":[44,150,154,159],"with":[48,80,166],"${\\alpha":[49,53,58],"_1}":[50],"\\ne":[51,55,60],"0$,":[52,56,85],"_2}":[54],"and":[57,86],"_3}":[59],"0$.":[61],"First,":[62],"give":[64],"recursive":[66],"construction":[67],"type":[73],"$\\left(":[74],"{{\\alpha":[75],"_1},{\\alpha":[76],"_2},{\\alpha":[77],"_3};{t_1},{t_2},{t_3}}":[78],"\\right)$":[79],"${t_1}":[81],"\\geq":[82,84,88,168],"1,{t_2}":[83],"${t_3}":[87],"1$.":[89],"Then,":[90],"show":[92,107,134],"types":[95],"corresponding":[97],"nonlinear":[102,143],"over":[103],"${\\mathbb{Z}_2}$.":[104],"Moreover,":[105],"that,":[108,135],"unlike":[109],"codes,":[112],"in":[113],"general,":[114],"family":[116,125],"does":[121],"not":[122,148],"include":[123],"\u21244-linear":[127],"or":[128],"${\\mathbb{Z}_8}$-linear":[129],"codes.":[131],"Actually,":[132],"example,":[137],"length":[139],"${2^{11}}$,":[140],"constructed":[142,162],"equivalent":[149],"each":[151],"other,":[152],"nor":[153,158],"any":[155,160],"Hadamard,":[157],"previously":[161],"${\\mathbb{Z}_{{2^s}}}$-linear":[163],"code,":[165],"$s":[167],"2$.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
