{"id":"https://openalex.org/W1572441187","doi":"https://doi.org/10.1007/11617983_32","title":"Hadamard Codes of Length 2 t s (s Odd). Rank and Kernel","display_name":"Hadamard Codes of Length 2 t s (s Odd). Rank and Kernel","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1572441187","doi":"https://doi.org/10.1007/11617983_32","mag":"1572441187"},"language":"en","primary_location":{"id":"doi:10.1007/11617983_32","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11617983_32","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5069038206","display_name":"Kevin T. Phelps","orcid":null},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin T. Phelps","raw_affiliation_strings":["Dept. of Mathematics and Statistics, Auburn University, Auburn","Department of Mathematics and Statistics, Auburn University, Auburn, AL#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics and Statistics, Auburn University, Auburn","institution_ids":["https://openalex.org/I82497590"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Auburn University, Auburn, AL#TAB#","institution_ids":["https://openalex.org/I82497590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082545070","display_name":"Josep Rif\u00e0","orcid":"https://orcid.org/0000-0001-9199-4001"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Josep Rif\u00e0","raw_affiliation_strings":["Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080668151","display_name":"Merc\u00e8 Villanueva","orcid":"https://orcid.org/0000-0001-6179-0833"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Merc\u00e8 Villanueva","raw_affiliation_strings":["Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.11957029,"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":"328","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9975000023841858,"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":0.9975000023841858,"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/T11130","display_name":"Coding theory and cryptography","score":0.9819999933242798,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9754999876022339,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.887056291103363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.668248176574707},{"id":"https://openalex.org/keywords/hadamard-code","display_name":"Hadamard code","score":0.636228621006012},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.62788325548172},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6248749494552612},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6151391267776489},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5452947020530701},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.47806575894355774},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.4108867049217224},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4102972447872162},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.29182863235473633},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.210493266582489},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12266659736633301},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.044480711221694946}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.887056291103363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.668248176574707},{"id":"https://openalex.org/C26693338","wikidata":"https://www.wikidata.org/wiki/Q1567339","display_name":"Hadamard code","level":3,"score":0.636228621006012},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.62788325548172},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6248749494552612},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6151391267776489},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5452947020530701},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.47806575894355774},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.4108867049217224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4102972447872162},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.29182863235473633},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.210493266582489},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12266659736633301},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.044480711221694946},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11617983_32","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11617983_32","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1517011653","https://openalex.org/W1519204501","https://openalex.org/W1606480398","https://openalex.org/W2064737342","https://openalex.org/W2081939650","https://openalex.org/W2104885095","https://openalex.org/W2143250996","https://openalex.org/W2159271156","https://openalex.org/W2915019512","https://openalex.org/W3101163237","https://openalex.org/W3139968900","https://openalex.org/W4211147273"],"related_works":["https://openalex.org/W2078905249","https://openalex.org/W2323505138","https://openalex.org/W1535286235","https://openalex.org/W173825516","https://openalex.org/W4226207720","https://openalex.org/W1579261672","https://openalex.org/W118486707","https://openalex.org/W2143250996","https://openalex.org/W1585730421","https://openalex.org/W2161857268"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
