{"id":"https://openalex.org/W4400104794","doi":"https://doi.org/10.48550/arxiv.2406.18325","title":"Linear codes with few weights over $\\mathbb{F}_{p}+u\\mathbb{F}_{p}$","display_name":"Linear codes with few weights over $\\mathbb{F}_{p}+u\\mathbb{F}_{p}$","publication_year":2024,"publication_date":"2024-06-26","ids":{"openalex":"https://openalex.org/W4400104794","doi":"https://doi.org/10.48550/arxiv.2406.18325"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2406.18325","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.18325","pdf_url":"https://arxiv.org/pdf/2406.18325","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2406.18325","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101398697","display_name":"Pavan Kumar","orcid":"https://orcid.org/0000-0001-5340-7777","observed_orcids":["https://orcid.org/0000-0001-5340-7777"]},"institutions":[{"id":"https://openalex.org/I171210897","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02","country_code":"IN","type":"education","lineage":["https://openalex.org/I171210897"]},{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kumar, Pavan","raw_affiliation_strings":["Department of Electronic Systems Engineering , Indian Institute of Science , Bengaluru 560012 , India","Department of Mathematics , Aligarh Muslim University , Aligarh - 202002 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Systems Engineering , Indian Institute of Science , Bengaluru 560012 , India","institution_ids":["https://openalex.org/I59270414"]},{"raw_affiliation_string":"Department of Mathematics , Aligarh Muslim University , Aligarh - 202002 , India","institution_ids":["https://openalex.org/I171210897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101895797","display_name":"Noor Mohammad Khan","orcid":"https://orcid.org/0000-0002-8360-5851","observed_orcids":["https://orcid.org/0000-0002-8360-5851"]},"institutions":[{"id":"https://openalex.org/I171210897","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02","country_code":"IN","type":"education","lineage":["https://openalex.org/I171210897"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Khan, Noor Mohammad","raw_affiliation_strings":["Department of Mathematics , Aligarh Muslim University , Aligarh - 202002 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Aligarh Muslim University , Aligarh - 202002 , India","institution_ids":["https://openalex.org/I171210897"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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":0.9994999766349792,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/linear-codes","display_name":"linear codes","score":0.9660000205039978},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"weight distribution","score":0.593999981880188},{"id":"https://openalex.org/keywords/trace-functions","display_name":"trace functions","score":0.546999990940094},{"id":"https://openalex.org/keywords/grayscale-images","display_name":"grayscale images","score":0.5339999794960022},{"id":"https://openalex.org/keywords/ring-extensions","display_name":"ring extensions","score":0.5709999799728394},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.31200000643730164}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5676071047782898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5044561624526978},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37309545278549194},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3624168038368225}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2406.18325","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.18325","pdf_url":"https://arxiv.org/pdf/2406.18325","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2406.18325","doi":"https://doi.org/10.48550/arxiv.2406.18325","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2406.18325","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2406.18325","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.18325","pdf_url":"https://arxiv.org/pdf/2406.18325","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4887626851","display_name":null,"funder_award_id":"11-04-2016-413564","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"}],"funders":[{"id":"https://openalex.org/F4320320767","display_name":"University Grants Commission","ror":"https://ror.org/04p800546"},{"id":"https://openalex.org/F4320321426","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400104794.pdf","grobid_xml":"https://content.openalex.org/works/W4400104794.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049"],"abstract_inverted_index":{"For":[0],"any":[1],"positive":[2],"integer":[3],"$m$":[4],"and":[5,38],"an":[6],"odd":[7],"prime":[8],"$p$;":[9],"let":[10],"$\\mathbb{F}_{q}+u\\mathbb{F}_{q}$,":[11],"where":[12],"$q=p^{m}$,":[13],"be":[14],"a":[15],"ring":[16,20],"extension":[17],"of":[18,48],"the":[19],"$\\mathbb{F}_{p}+u\\mathbb{F}_{p}.$":[21],"In":[22],"this":[23],"paper,":[24],"we":[25],"construct":[26],"linear":[27],"codes":[28],"over":[29],"$\\mathbb{F}_{p}+u\\mathbb{F}_{p}$":[30],"by":[31,44],"using":[32],"trace":[33],"function":[34],"defined":[35],"on":[36],"$\\mathbb{F}_{q}+u\\mathbb{F}_{q}$":[37],"determine":[39],"their":[40,49],"Hamming":[41],"weight":[42],"distributions":[43,47],"employing":[45],"symplectic-weight":[46],"Gray":[50],"images.":[51]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2025-10-10T00:00:00"}
