{"id":"https://openalex.org/W4387950554","doi":"https://doi.org/10.1371/journal.pone.0293294","title":"Features of digital signal processing algorithms using Galois fields GF(2n+1)","display_name":"Features of digital signal processing algorithms using Galois fields GF(2n+1)","publication_year":2023,"publication_date":"2023-10-25","ids":{"openalex":"https://openalex.org/W4387950554","doi":"https://doi.org/10.1371/journal.pone.0293294","pmid":"https://pubmed.ncbi.nlm.nih.gov/37878646","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/10599577"},"language":"en","primary_location":{"id":"doi:10.1371/journal.pone.0293294","doi":"https://doi.org/10.1371/journal.pone.0293294","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pone.0293294","pdf_url":"https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0293294&type=printable","source":{"id":"https://openalex.org/S202381698","display_name":"PLoS ONE","issn_l":"1932-6203","issn":["1932-6203"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","erih-plus","jufo-1","ki-jl-1","medline","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS ONE","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0293294&type=printable","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030471618","display_name":"Ibragim Esenovich Suleimenov","orcid":"https://orcid.org/0000-0002-7274-029X","observed_orcids":["https://orcid.org/0000-0002-7274-029X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ibragim E. Suleimenov","raw_affiliation_strings":["National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-7274-029X","affiliations":[{"raw_affiliation_string":"National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026106321","display_name":"Yelizaveta Sergeevna Vitulyova","orcid":"https://orcid.org/0000-0002-6075-4870","observed_orcids":["https://orcid.org/0000-0002-6075-4870"]},"institutions":[{"id":"https://openalex.org/I247491477","display_name":"Almaty University of Power Engineering and Telecommunications","ror":"https://ror.org/020d95911","country_code":"KZ","type":"education","lineage":["https://openalex.org/I247491477"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Yelizaveta S. Vitulyova","raw_affiliation_strings":["Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev, Almaty, Republic of Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-6075-4870","affiliations":[{"raw_affiliation_string":"Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev, Almaty, Republic of Kazakhstan","institution_ids":["https://openalex.org/I247491477"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003081546","display_name":"Dinara Matrassulova","orcid":"https://orcid.org/0000-0002-0646-6333","observed_orcids":["https://orcid.org/0000-0002-0646-6333"]},"institutions":[{"id":"https://openalex.org/I247491477","display_name":"Almaty University of Power Engineering and Telecommunications","ror":"https://ror.org/020d95911","country_code":"KZ","type":"education","lineage":["https://openalex.org/I247491477"]}],"countries":["KZ"],"is_corresponding":true,"raw_author_name":"Dinara K. Matrassulova","raw_affiliation_strings":["Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev, Almaty, Republic of Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-0646-6333","affiliations":[{"raw_affiliation_string":"Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev, Almaty, Republic of Kazakhstan","institution_ids":["https://openalex.org/I247491477"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003081546"],"corresponding_institution_ids":["https://openalex.org/I247491477"],"apc_list":{"value":1805,"currency":"USD","value_usd":1805},"apc_paid":{"value":1805,"currency":"USD","value_usd":1805},"fwci":1.4546,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82729059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"18","issue":"10","first_page":"e0293294","last_page":"e0293294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/digital-signal-processing-algorithms","display_name":"digital signal processing algorithms","score":0.8040000200271606},{"id":"https://openalex.org/keywords/modular-multiplication","display_name":"modular multiplication","score":0.7160000205039978},{"id":"https://openalex.org/keywords/mersenne-numbers","display_name":"Mersenne numbers","score":0.8769999742507935}],"concepts":[{"id":"https://openalex.org/C29641680","wikidata":"https://www.wikidata.org/wiki/Q186875","display_name":"Mersenne prime","level":2,"score":0.8154059648513794},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.741737961769104},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.6596828699111938},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6012362241744995},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5609214901924133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5477055311203003},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5474026203155518},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5165754556655884},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5003669261932373},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.45671525597572327},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4458315968513489},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.4324336647987366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39051148295402527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3455030918121338},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2601693272590637},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.20699718594551086},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":5,"locations":[{"id":"doi:10.1371/journal.pone.0293294","doi":"https://doi.org/10.1371/journal.pone.0293294","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pone.0293294","pdf_url":"https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0293294&type=printable","source":{"id":"https://openalex.org/S202381698","display_name":"PLoS ONE","issn_l":"1932-6203","issn":["1932-6203"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","erih-plus","jufo-1","ki-jl-1","medline","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS ONE","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:10599577","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10599577","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10599577/pdf/pone.0293294.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLoS One","raw_type":"Text"},{"id":"pmid:37878646","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37878646","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PloS one","raw_type":"Journal Article"},{"id":"pmh:oai:RePEc:plo:pone00:0293294","doi":null,"is_oa":false,"landing_page_url":"https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0293294","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:86a5e52dfaf74b21824441b34a977843","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/86a5e52dfaf74b21824441b34a977843","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"PLoS ONE, Vol 18, Iss 10, p e0293294 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1371/journal.pone.0293294","doi":"https://doi.org/10.1371/journal.pone.0293294","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pone.0293294","pdf_url":"https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0293294&type=printable","source":{"id":"https://openalex.org/S202381698","display_name":"PLoS ONE","issn_l":"1932-6203","issn":["1932-6203"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","erih-plus","jufo-1","ki-jl-1","medline","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS ONE","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310481","display_name":"Uddannelses- og Forskningsministeriet","ror":"https://ror.org/03ge1nb22"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387950554.pdf","grobid_xml":"https://content.openalex.org/works/W4387950554.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W2024511827","https://openalex.org/W2047866494","https://openalex.org/W2095595785","https://openalex.org/W2800373564","https://openalex.org/W2900469032","https://openalex.org/W2939073427","https://openalex.org/W2952568054","https://openalex.org/W2984441440","https://openalex.org/W2991280424","https://openalex.org/W3025838941","https://openalex.org/W3082987616","https://openalex.org/W3095988609","https://openalex.org/W3110186717","https://openalex.org/W3186038803","https://openalex.org/W3191729854","https://openalex.org/W3199815534","https://openalex.org/W4206955021","https://openalex.org/W4206989817","https://openalex.org/W4283216815","https://openalex.org/W4285281503","https://openalex.org/W4297799210","https://openalex.org/W4317569126"],"related_works":["https://openalex.org/W4400330481","https://openalex.org/W1828919796","https://openalex.org/W2046857030","https://openalex.org/W2091485067","https://openalex.org/W830130808","https://openalex.org/W7100434632","https://openalex.org/W4301373675","https://openalex.org/W1991732986","https://openalex.org/W3178283545","https://openalex.org/W2228442681"],"abstract_inverted_index":{"An":[0],"alternating":[1],"representation":[2,30],"of":[3,20],"integers":[4],"in":[5,10],"binary":[6],"form":[7],"is":[8,25,45,64],"proposed,":[9],"which":[11],"the":[12,56,60,88],"numbers":[13,36,69],"-1":[14],"and":[15,22],"+1":[16],"are":[17],"used":[18],"instead":[19],"zeros":[21],"ones.":[23],"It":[24,63],"shown":[26,65],"that":[27,66],"such":[28,42,68],"a":[29,49,70,92],"creates":[31],"considerable":[32],"convenience":[33],"for":[34,67,73],"multiplication":[35,50,57,89],"modulo":[37,52,59,91],"p":[38,95],"=":[39,96],"2n+1.":[40],"For":[41],"numbers,":[43],"it":[44],"possible":[46],"to":[47,55,86,98],"implement":[48],"algorithm":[51,58,72,81],"p,":[53],"similar":[54],"Mersenne":[61],"number.":[62],"simple":[71],"digital":[74],"logarithm":[75],"calculations":[76],"may":[77],"be":[78],"proposed.":[79],"This":[80],"allows,":[82],"among":[83],"other":[84],"things,":[85],"reduce":[87],"operation":[90],"prime":[93],"number":[94],"2n+1":[97],"an":[99],"addition":[100],"operation.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2023-10-27T00:00:00"}
