{"id":"https://openalex.org/W4389213139","doi":"https://doi.org/10.3934/amc.2023053","title":"Some constructions of $l$-Galois LCD codes","display_name":"Some constructions of $l$-Galois LCD codes","publication_year":2023,"publication_date":"2023-11-30","ids":{"openalex":"https://openalex.org/W4389213139","doi":"https://doi.org/10.3934/amc.2023053"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2023053","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2023053","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=65644c13eca2737fc4ef4e32","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=65644c13eca2737fc4ef4e32","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070333650","display_name":"Shikha Yadav","orcid":"https://orcid.org/0000-0002-2466-4966"},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Shikha Yadav","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Patna Patna, Bihar-801106, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna Patna, Bihar-801106, India","institution_ids":["https://openalex.org/I132153292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024719879","display_name":"Indibar Debnath","orcid":"https://orcid.org/0009-0003-2511-5066"},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Indibar Debnath","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar-801106, India","Department of Mathematics, Indian Institute of Technology Patna Patna, Bihar-801106, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar-801106, India","institution_ids":["https://openalex.org/I132153292"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna Patna, Bihar-801106, India","institution_ids":["https://openalex.org/I132153292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065837828","display_name":"Om Prakash","orcid":"https://orcid.org/0000-0002-6512-4229"},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Om Prakash","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar-801106, India","Department of Mathematics, Indian Institute of Technology Patna Patna, Bihar-801106, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar-801106, India","institution_ids":["https://openalex.org/I132153292"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna Patna, Bihar-801106, India","institution_ids":["https://openalex.org/I132153292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070333650"],"corresponding_institution_ids":["https://openalex.org/I132153292"],"apc_list":null,"apc_paid":null,"fwci":1.049,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81867642,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"19","issue":"1","first_page":"227","last_page":"244"},"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":0.9966999888420105,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.8637259006500244},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6622751355171204},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.6550675630569458},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.5335358381271362},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.49749401211738586},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44308027625083923},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4414098858833313},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3767205476760864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3730695843696594},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11502593755722046},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07709541916847229}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8637259006500244},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6622751355171204},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.6550675630569458},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.5335358381271362},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.49749401211738586},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44308027625083923},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4414098858833313},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3767205476760864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3730695843696594},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11502593755722046},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07709541916847229},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2023053","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2023053","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=65644c13eca2737fc4ef4e32","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.2023053","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2023053","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=65644c13eca2737fc4ef4e32","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":[{"id":"https://openalex.org/F4320319144","display_name":"Indian Institute of Technology, Patna","ror":"https://ror.org/01ft5vz71"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389213139.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W2016652749","https://openalex.org/W2026316191","https://openalex.org/W2187204584","https://openalex.org/W2773561837","https://openalex.org/W2787275646","https://openalex.org/W2891992737","https://openalex.org/W2948381779","https://openalex.org/W2962682082","https://openalex.org/W2963616848","https://openalex.org/W2964238800","https://openalex.org/W2989678375","https://openalex.org/W2993213577","https://openalex.org/W3007455756","https://openalex.org/W3122090441","https://openalex.org/W3185223764","https://openalex.org/W3190051971","https://openalex.org/W4213240612","https://openalex.org/W4283360609","https://openalex.org/W4285083959","https://openalex.org/W4289516718","https://openalex.org/W4306697274","https://openalex.org/W4312583145","https://openalex.org/W6600351811","https://openalex.org/W6602670149","https://openalex.org/W6732987287","https://openalex.org/W6779765214"],"related_works":["https://openalex.org/W2890903969","https://openalex.org/W2186975062","https://openalex.org/W4321854132","https://openalex.org/W3198007960","https://openalex.org/W4322759337","https://openalex.org/W1559823796","https://openalex.org/W2377672155","https://openalex.org/W3081504594","https://openalex.org/W2064186082","https://openalex.org/W4387838227"],"abstract_inverted_index":{"Let":[0],"$":[1,3,9,11,14,18,22,24,26,42,44,72,74,77,85,87,89],"\\mathbb{F}_q":[2,43],"be":[4],"the":[5,54,70,91,97,106,148],"finite":[6,119],"field":[7],"with":[8],"q":[10,15],"elements":[12],"where":[13,86],"=":[16,79],"p^m":[17],"for":[19,75],"some":[20,35,118],"prime":[21],"p":[23],"and":[25,101,140],"m":[27],"&gt;0":[28],"$.":[29],"In":[30],"this":[31],"article,":[32],"we":[33,52,68,122,136],"provide":[34],"constructions":[36],"of":[37,47,59,108,126,150],"Galois":[38,55,98,127,143],"LCD":[39,111,128,144],"codes":[40,129,145],"over":[41,117],"in":[45,130],"terms":[46],"their":[48],"generator":[49],"matrices.":[50],"Here,":[51],"consider":[53],"inner":[56,63],"product":[57],"instead":[58],"Euclidean":[60,110],"or":[61],"Hermitian":[62],"products.":[64],"For":[65],"these":[66],"constructions,":[67],"use":[69,102],"matrix":[71],"A":[73],"which":[76],"A[\\sigma^{m-l}(A)]^t":[78],"I,\\;":[80],"0\\leq":[81],"l":[82],"\\leq":[83],"m-1":[84],"\\sigma":[88],"is":[90],"Frobenius":[92],"map.":[93],"We":[94],"also":[95],"define":[96],"self-dual":[99],"basis":[100],"it":[103],"to":[104,146],"show":[105,147],"existence":[107],"a":[109,114,131],"code":[112,116],"from":[113],"linear":[115],"field.":[120],"Further,":[121],"present":[123],"an":[124],"application":[125],"multi-secret":[132],"sharing":[133],"scheme.":[134],"Besides,":[135],"obtain":[137],"several":[138],"optimal":[139,142],"almost":[141],"importance":[149],"our":[151],"results.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":6}],"updated_date":"2026-01-20T17:24:06.736184","created_date":"2025-10-10T00:00:00"}
