{"id":"https://openalex.org/W4396930193","doi":"https://doi.org/10.3934/amc.2024021","title":"Weight hierarchies of 3-weight linear codes from <i>p</i>-ary quadratic functions","display_name":"Weight hierarchies of 3-weight linear codes from <i>p</i>-ary quadratic functions","publication_year":2024,"publication_date":"2024-05-15","ids":{"openalex":"https://openalex.org/W4396930193","doi":"https://doi.org/10.3934/amc.2024021"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2024021","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/amc.2024021","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=6641b931475da12c51d5e3f7","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=6641b931475da12c51d5e3f7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074833902","display_name":"Xiumei Li","orcid":"https://orcid.org/0000-0003-3027-8129"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiumei Li","raw_affiliation_strings":["School of Mathematical Sciences, Qufu Normal University, Qufu Shandong, 273165, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Qufu Normal University, Qufu Shandong, 273165, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100325764","display_name":"Fei Li","orcid":"https://orcid.org/0000-0001-7394-5273"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]},{"id":"https://openalex.org/I188935350","display_name":"Anhui University of Finance and Economics","ror":"https://ror.org/0152zzg30","country_code":"CN","type":"education","lineage":["https://openalex.org/I188935350"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fei Li","raw_affiliation_strings":["Faculty of School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu Anhui, 233030, China","School of Mathematical Sciences, Qufu Normal University, Qufu Shandong, 273165, China"],"affiliations":[{"raw_affiliation_string":"Faculty of School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu Anhui, 233030, China","institution_ids":["https://openalex.org/I188935350"]},{"raw_affiliation_string":"School of Mathematical Sciences, Qufu Normal University, Qufu Shandong, 273165, China","institution_ids":["https://openalex.org/I202126657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074833902"],"corresponding_institution_ids":["https://openalex.org/I202126657"],"apc_list":null,"apc_paid":null,"fwci":0.3626,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62944561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"19","issue":"2","first_page":"736","last_page":"747"},"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":0.9740999937057495,"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/T13437","display_name":"Mechanisms of cancer metastasis","score":0.9624999761581421,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9341124296188354},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6004226803779602},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4303280711174011},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37979254126548767},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37273573875427246},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.053225427865982056}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9341124296188354},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6004226803779602},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4303280711174011},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37979254126548767},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37273573875427246},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.053225427865982056}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2024021","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/amc.2024021","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=6641b931475da12c51d5e3f7","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2024021","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/amc.2024021","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=6641b931475da12c51d5e3f7","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396930193.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W760976637","https://openalex.org/W1528165011","https://openalex.org/W1969564787","https://openalex.org/W1973992189","https://openalex.org/W1978435645","https://openalex.org/W2004865039","https://openalex.org/W2008721293","https://openalex.org/W2041404600","https://openalex.org/W2098933212","https://openalex.org/W2111616448","https://openalex.org/W2113800264","https://openalex.org/W2120756519","https://openalex.org/W2127558904","https://openalex.org/W2157171589","https://openalex.org/W2163834165","https://openalex.org/W2293931389","https://openalex.org/W2569763494","https://openalex.org/W2810143492","https://openalex.org/W2962947453","https://openalex.org/W2963169017","https://openalex.org/W2963905861","https://openalex.org/W2982774419","https://openalex.org/W3083222302","https://openalex.org/W3099133195","https://openalex.org/W3105418885","https://openalex.org/W3159210038","https://openalex.org/W3208647221","https://openalex.org/W3217544812","https://openalex.org/W4233185505","https://openalex.org/W4285155006","https://openalex.org/W4320480952"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"The":[0],"weight":[1,62],"hierarchy":[2],"of":[3,52,66],"a":[4,34,50],"linear":[5,57],"code":[6],"has":[7],"been":[8],"an":[9],"important":[10],"research":[11],"topic":[12],"in":[13,20,72],"coding":[14],"theory":[15],"since":[16],"Wei's":[17],"original":[18],"work":[19],"1991.":[21],"By":[22],"choosing":[23],"$":[24,32,38,40,42,44,54],"D":[25],"=":[26,30],"\\Big\\{(x,y)\\in":[27],"\\Big({\\mathbb{F}}_{p^{s_1}}\\times{\\mathbb{F}}_{p^{s_2}}\\Big)\\Big\\backslash\\{(0,0)\\}:":[28],"f(x)+g(y)":[29],"0\\Big\\}":[31],"as":[33],"defining":[35],"set,":[36],"where":[37],"f(x)":[39],"and":[41,59],"g(y)":[43],"are":[45],"quadratic":[46],"forms,":[47],"we":[48],"construct":[49],"family":[51],"3-weight":[53],"p":[55],"$-ary":[56],"codes":[58,68],"determine":[60],"the":[61,67],"hierarchies":[63],"completely.":[64],"Most":[65],"can":[69],"be":[70],"used":[71],"secret":[73],"sharing":[74],"schemes.":[75]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}