{"id":"https://openalex.org/W2789458931","doi":"https://doi.org/10.3934/amc.2018008","title":"Trace description and Hamming weights of irreducible constacyclic codes","display_name":"Trace description and Hamming weights of irreducible constacyclic codes","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2789458931","doi":"https://doi.org/10.3934/amc.2018008","mag":"2789458931"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2018008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018008","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.2018008","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100729984","display_name":"Anuradha Sharma","orcid":"https://orcid.org/0000-0002-0133-8658"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anuradha Sharma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078939169","display_name":"Saroj Rani","orcid":"https://orcid.org/0000-0003-1580-985X"},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Saroj Rani","raw_affiliation_strings":["Department of Mathematics, IIT Delhi,  New Delhi, 110016, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IIT Delhi,  New Delhi, 110016, India","institution_ids":["https://openalex.org/I68891433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.02150684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"12","issue":"1","first_page":"123","last_page":"141"},"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":0.9955000281333923,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9882000088691711,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8292480111122131},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.6630662679672241},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6392341256141663},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5707874298095703},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5593885183334351},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.5491970181465149},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5407571196556091},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.5234505534172058},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.5028166174888611},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4836310148239136},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4568912982940674},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42040693759918213},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.41981634497642517},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.3967646062374115},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3486226201057434},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09536293148994446}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8292480111122131},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6630662679672241},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6392341256141663},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5707874298095703},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5593885183334351},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.5491970181465149},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5407571196556091},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.5234505534172058},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.5028166174888611},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4836310148239136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4568912982940674},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42040693759918213},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.41981634497642517},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.3967646062374115},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3486226201057434},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09536293148994446},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2018008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018008","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.2018008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018008","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":16,"referenced_works":["https://openalex.org/W834619772","https://openalex.org/W1496636054","https://openalex.org/W1517017194","https://openalex.org/W1961683267","https://openalex.org/W1973986860","https://openalex.org/W2004537556","https://openalex.org/W2025489892","https://openalex.org/W2028984939","https://openalex.org/W2056890992","https://openalex.org/W2057274275","https://openalex.org/W2058618212","https://openalex.org/W2064494467","https://openalex.org/W2118120045","https://openalex.org/W2161127475","https://openalex.org/W2952919143","https://openalex.org/W3004074467"],"related_works":["https://openalex.org/W2963553930","https://openalex.org/W2963243225","https://openalex.org/W2238578788","https://openalex.org/W2157171589","https://openalex.org/W2111330432","https://openalex.org/W2951643466","https://openalex.org/W4380714746","https://openalex.org/W2740543340","https://openalex.org/W2268856369","https://openalex.org/W2964136540"],"abstract_inverted_index":{"Irreducible":[0],"constacyclic":[1,24,63,78,94,107],"codes":[2,25,64,108],"constitute":[3],"an":[4,53],"important":[5],"family":[6],"of":[7,22,26,34,60,65],"error-correcting":[8],"codesand":[9],"have":[10],"applications":[11],"in":[12,92,115],"space":[13],"communications.In":[14],"this":[15],"paper,":[16],"we":[17,55,102],"provide":[18],"a":[19,40,46,73],"trace":[20],"description":[21],"irreducible":[23,62,77,93,106],"length":[27,66],"$n$":[28,38,67],"over":[29,68],"the":[30,88,111],"finite":[31],"field":[32],"$\\mathbb{F}_{q}$":[33],"order":[35],"$q,$":[36],"where":[37],"is":[39,45],"positive":[41],"integer":[42],"and":[43,80,84],"$q$":[44],"prime":[47],"power":[48],"coprime":[49],"to":[50],"$n.$":[51],"As":[52],"application,":[54],"determine":[56],"Hamming":[57,90],"weight":[58],"distributions":[59],"some":[61,104],"$\\mathbb{F}_{q}.$":[69],"We":[70],"also":[71],"derive":[72],"weight-divisibility":[74],"theorem":[75],"for":[76],"codes,":[79],"obtain":[81],"both":[82],"lower":[83],"upper":[85],"bounds":[86,113],"on":[87],"non-zero":[89],"weights":[91],"codes.":[95],"Besides":[96],"illustrating":[97],"our":[98],"results":[99],"with":[100],"examples,":[101],"list":[103],"optimal":[105],"that":[109],"attain":[110],"distance":[112],"given":[114],"Grassl's":[116],"Table":[117],"[8].":[118]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
