{"id":"https://openalex.org/W4205349434","doi":"https://doi.org/10.3934/mfc.2021041","title":"Two-weight and three-weight linear codes constructed from Weil sums","display_name":"Two-weight and three-weight linear codes constructed from Weil sums","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4205349434","doi":"https://doi.org/10.3934/mfc.2021041"},"language":"en","primary_location":{"id":"doi:10.3934/mfc.2021041","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2021041","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=7efdd28e-ff33-40a5-b006-8628e900bfb0","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=7efdd28e-ff33-40a5-b006-8628e900bfb0","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051160274","display_name":"Tonghui Zhang","orcid":"https://orcid.org/0000-0001-5356-8167"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tonghui Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110018220","display_name":"Hong Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong Lu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033644023","display_name":"Shudi Yang","orcid":"https://orcid.org/0000-0003-1536-4627"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shudi Yang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051160274"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5552,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70582422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"5","issue":"2","first_page":"129","last_page":"129"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9916999936103821,"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/secret-sharing","display_name":"Secret sharing","score":0.6899834871292114},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6220719814300537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.548630952835083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5247716307640076},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5234783887863159},{"id":"https://openalex.org/keywords/authentication","display_name":"Authentication (law)","score":0.4864180088043213},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.48006686568260193},{"id":"https://openalex.org/keywords/association-scheme","display_name":"Association scheme","score":0.46461713314056396},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35087066888809204},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3183220624923706},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3110862672328949},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2402331829071045},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.23924469947814941},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.11223989725112915},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.07219409942626953},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.05087229609489441}],"concepts":[{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.6899834871292114},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6220719814300537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.548630952835083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5247716307640076},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5234783887863159},{"id":"https://openalex.org/C148417208","wikidata":"https://www.wikidata.org/wiki/Q4825882","display_name":"Authentication (law)","level":2,"score":0.4864180088043213},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.48006686568260193},{"id":"https://openalex.org/C73361133","wikidata":"https://www.wikidata.org/wiki/Q4810150","display_name":"Association scheme","level":2,"score":0.46461713314056396},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35087066888809204},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3183220624923706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3110862672328949},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2402331829071045},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.23924469947814941},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.11223989725112915},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.07219409942626953},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.05087229609489441}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/mfc.2021041","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2021041","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=7efdd28e-ff33-40a5-b006-8628e900bfb0","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/mfc.2021041","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2021041","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=7efdd28e-ff33-40a5-b006-8628e900bfb0","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4205349434.pdf","grobid_xml":"https://content.openalex.org/works/W4205349434.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1471103927","https://openalex.org/W1578199253","https://openalex.org/W1999598167","https://openalex.org/W2092900268","https://openalex.org/W2113800264","https://openalex.org/W2141420453","https://openalex.org/W2163834165","https://openalex.org/W2425228145","https://openalex.org/W2486639169","https://openalex.org/W2801800941","https://openalex.org/W2808625055","https://openalex.org/W2911767394","https://openalex.org/W2962947453","https://openalex.org/W2970097841","https://openalex.org/W3007079256","https://openalex.org/W3009266644","https://openalex.org/W3090088093","https://openalex.org/W3090806472","https://openalex.org/W3099133195","https://openalex.org/W3134985447","https://openalex.org/W3147043509","https://openalex.org/W3171545851","https://openalex.org/W3196890818","https://openalex.org/W4206775542"],"related_works":["https://openalex.org/W3119163369","https://openalex.org/W135568846","https://openalex.org/W2460434904","https://openalex.org/W1789159349","https://openalex.org/W2113911300","https://openalex.org/W2090381698","https://openalex.org/W832867880","https://openalex.org/W2147254059","https://openalex.org/W2151857680","https://openalex.org/W4386066307"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>Linear":[1],"codes":[2,31,50],"with":[3],"few":[4],"weights":[5],"are":[6,51,62],"widely":[7],"used":[8],"in":[9],"strongly":[10],"regular":[11],"graphs,":[12],"secret":[13,59],"sharing":[14,60],"schemes,":[15],"association":[16],"schemes":[17,61],"and":[18,28,46],"authentication":[19],"codes.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24],"construct":[25],"several":[26],"two-weight":[27],"three-weight":[29],"linear":[30],"over":[32],"finite":[33],"fields":[34],"by":[35],"choosing":[36],"suitable":[37],"different":[38],"defining":[39],"sets.":[40],"We":[41],"also":[42,63],"give":[43],"some":[44,47],"examples":[45],"of":[48],"the":[49],"optimal":[52],"or":[53],"almost":[54],"optimal.":[55],"Their":[56],"applications":[57],"to":[58],"investigated.</p>":[64]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}