{"id":"https://openalex.org/W4404770294","doi":"https://doi.org/10.3934/amc.2024049","title":"Several classes of BCH and negacyclic BCH codes of length <inline-formula><tex-math id=\"M1\">$n = \\frac{q^{m}-1}{2}$</tex-math></inline-formula>","display_name":"Several classes of BCH and negacyclic BCH codes of length <inline-formula><tex-math id=\"M1\">$n = \\frac{q^{m}-1}{2}$</tex-math></inline-formula>","publication_year":2024,"publication_date":"2024-11-27","ids":{"openalex":"https://openalex.org/W4404770294","doi":"https://doi.org/10.3934/amc.2024049"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2024049","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024049","pdf_url":null,"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://doi.org/10.3934/amc.2024049","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5098970643","display_name":"Mengchen Lian","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mengchen Lian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109347844","display_name":"Shixin Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shixin Zhu","raw_affiliation_strings":["School of Mathematics, HeFei University of Technology, Hefei 230601, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, HeFei University of Technology, Hefei 230601, China","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5098970643"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3862,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.69441225,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"19","issue":"4","first_page":"1192","last_page":"1210"},"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":0.9984999895095825,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9876999855041504,"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/bch-code","display_name":"BCH code","score":0.9723210334777832},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9035024642944336},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4178123474121094},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3685135841369629},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11165004968643188},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.08446282148361206}],"concepts":[{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.9723210334777832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9035024642944336},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4178123474121094},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3685135841369629},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11165004968643188},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.08446282148361206}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2024049","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024049","pdf_url":null,"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.2024049","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024049","pdf_url":null,"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":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W95404506","https://openalex.org/W1538532843","https://openalex.org/W1680549012","https://openalex.org/W2036538870","https://openalex.org/W2095755044","https://openalex.org/W2118897868","https://openalex.org/W2130499429","https://openalex.org/W2164604678","https://openalex.org/W2304375173","https://openalex.org/W2489562663","https://openalex.org/W2491978534","https://openalex.org/W2734604647","https://openalex.org/W2767066543","https://openalex.org/W2963166889","https://openalex.org/W2964110229","https://openalex.org/W2964238317","https://openalex.org/W2971705356","https://openalex.org/W2984241739","https://openalex.org/W3004315610","https://openalex.org/W3014515211","https://openalex.org/W3203404927","https://openalex.org/W3212752911","https://openalex.org/W4324117810","https://openalex.org/W4353065016","https://openalex.org/W4378530344","https://openalex.org/W4386299194","https://openalex.org/W4388830301","https://openalex.org/W4390577237","https://openalex.org/W4391707609"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2912502034","https://openalex.org/W2319574489","https://openalex.org/W2035908476","https://openalex.org/W2506979107","https://openalex.org/W4239727543","https://openalex.org/W2612882049","https://openalex.org/W2284101512","https://openalex.org/W1604083761","https://openalex.org/W2129090975"],"abstract_inverted_index":{"BCH":[0,25,28,37,87,113],"codes":[1,8,88],"are":[2,110],"an":[3],"important":[4],"class":[5],"of":[6,30,43,85,120,133],"linear":[7],"and":[9,15,27,62,98,130],"find":[10],"extensive":[11],"utilization":[12],"in":[13],"communication":[14],"disk":[16],"storage":[17],"systems.":[18],"This":[19],"paper":[20],"mainly":[21],"analyzes":[22],"the":[23,41,83,117,131],"negacyclic":[24,36,86],"code":[26,29,122,135],"length":[31],"$":[32,44,50,52,63,68,69,77,89,94,99,104,106,109,123,129,136,143],"\\frac{q^m-1}{2}":[33],"$.":[34,81,148],"For":[35,112],"code,":[38,114],"we":[39,115],"give":[40,116],"dimensions":[42,84],"\\mathcal{C}_{(n,":[45,90,100],"-1,":[46,91,101],"\\left\\lceil":[47,78],"\\frac{\\delta+1}{2}\\right\\rceil,":[48],"0)}":[49,93],"for":[51],"\\delta":[53,64,145],"=":[54,65],"a\\frac{q^m-1}{q-1},":[55],"aq^{m-1}-1":[56],"$($":[57],"1\\leq":[58,72],"a":[59],"<\\frac{q-1}{2}":[60],"$)":[61],"a\\frac{q^m-1}{q-1}+b\\frac{q^m-1}{q^2-1},":[66],"aq^{m-1}+(a+b)q^{m-2}-1":[67],"(2\\mid":[70],"m,":[71],"a+b":[73],"\\leq":[74,146],"q-1":[75],"$,":[76,141],"\\frac{q-a-2}{2}\\right\\rceil\\geq":[79],"1)":[80],"Furthermore,":[82],"\\delta,":[92,102,127,139],"with":[95,105],"few":[96],"nonzeros":[97],"b)}":[103],"b\\neq":[107],"0":[108],"settled.":[111],"weight":[118],"distribution":[119],"extended":[121],"\\overline{":[124],"\\mathcal{C}}_{(n,":[125],"1,":[126,138],"1)}":[128,140],"parameters":[132],"dual":[134],"\\mathcal{C}^{\\perp}_{(n,":[137],"where":[142],"\\delta_2\\leq":[144],"\\delta_1":[147]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2024-11-28T00:00:00"}