{"id":"https://openalex.org/W2553287553","doi":"https://doi.org/10.1007/s00200-016-0307-6","title":"Affine equivalence and non-linearity of permutations over $$\\mathbb Z_n$$ Z n","display_name":"Affine equivalence and non-linearity of permutations over $$\\mathbb Z_n$$ Z n","publication_year":2016,"publication_date":"2016-11-17","ids":{"openalex":"https://openalex.org/W2553287553","doi":"https://doi.org/10.1007/s00200-016-0307-6","mag":"2553287553"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-016-0307-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-016-0307-6","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101868886","display_name":"Yogesh Kumar","orcid":"https://orcid.org/0000-0003-4203-8958"},"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":true,"raw_author_name":"Yogesh Kumar","raw_affiliation_strings":["Department of Mathematics, IIT Delhi, New Delhi, 110016, India","Department of Mathematics, IIT Delhi, New Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IIT Delhi, New Delhi, 110016, India","institution_ids":["https://openalex.org/I68891433"]},{"raw_affiliation_string":"Department of Mathematics, IIT Delhi, New Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009290876","display_name":"P. R. Mishra","orcid":"https://orcid.org/0000-0003-0473-6616"},"institutions":[{"id":"https://openalex.org/I1340206300","display_name":"Defence Research and Development Organisation","ror":"https://ror.org/05k37v296","country_code":"IN","type":"government","lineage":["https://openalex.org/I1340206300","https://openalex.org/I4210150591"]},{"id":"https://openalex.org/I4210120887","display_name":"Scientific Analysis Group","ror":"https://ror.org/02rpzt041","country_code":"IN","type":"facility","lineage":["https://openalex.org/I1340206300","https://openalex.org/I4210120887","https://openalex.org/I4210150591"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"P. R. Mishra","raw_affiliation_strings":["Scientific Analysis Group, Defence Research and Development Organisation, Metcalfe House, New Delhi, 110054, India","Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific Analysis Group, Defence Research and Development Organisation, Metcalfe House, New Delhi, 110054, India","institution_ids":["https://openalex.org/I4210120887","https://openalex.org/I1340206300"]},{"raw_affiliation_string":"Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, India","institution_ids":["https://openalex.org/I4210120887","https://openalex.org/I1340206300"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009805746","display_name":"N. Rajesh Pillai","orcid":null},"institutions":[{"id":"https://openalex.org/I1340206300","display_name":"Defence Research and Development Organisation","ror":"https://ror.org/05k37v296","country_code":"IN","type":"government","lineage":["https://openalex.org/I1340206300","https://openalex.org/I4210150591"]},{"id":"https://openalex.org/I4210120887","display_name":"Scientific Analysis Group","ror":"https://ror.org/02rpzt041","country_code":"IN","type":"facility","lineage":["https://openalex.org/I1340206300","https://openalex.org/I4210120887","https://openalex.org/I4210150591"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"N. Rajesh Pillai","raw_affiliation_strings":["Scientific Analysis Group, Defence Research and Development Organisation, Metcalfe House, New Delhi, 110054, India","Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific Analysis Group, Defence Research and Development Organisation, Metcalfe House, New Delhi, 110054, India","institution_ids":["https://openalex.org/I4210120887","https://openalex.org/I1340206300"]},{"raw_affiliation_string":"Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, India","institution_ids":["https://openalex.org/I4210120887","https://openalex.org/I1340206300"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050620780","display_name":"R. K. Sharma","orcid":"https://orcid.org/0000-0001-5666-4103"},"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":true,"raw_author_name":"R. K. Sharma","raw_affiliation_strings":["Department of Mathematics, IIT Delhi, New Delhi, 110016, India","Department of Mathematics, IIT Delhi, New Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IIT Delhi, New Delhi, 110016, India","institution_ids":["https://openalex.org/I68891433"]},{"raw_affiliation_string":"Department of Mathematics, IIT Delhi, New Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009290876","https://openalex.org/A5009805746","https://openalex.org/A5050620780","https://openalex.org/A5101868886"],"corresponding_institution_ids":["https://openalex.org/I1340206300","https://openalex.org/I4210120887","https://openalex.org/I68891433"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.08006926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"3","first_page":"257","last_page":"279"},"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":0.9997000098228455,"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":0.9968000054359436,"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/affine-transformation","display_name":"Affine transformation","score":0.698725700378418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6764189004898071},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6693631410598755},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.5983447432518005},{"id":"https://openalex.org/keywords/cipher","display_name":"Cipher","score":0.545381486415863},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5210732221603394},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5085300207138062},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5046635866165161},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.43974971771240234},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.4205129146575928},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25366851687431335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2053413689136505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11015009880065918},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.08080118894577026}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.698725700378418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6764189004898071},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6693631410598755},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.5983447432518005},{"id":"https://openalex.org/C2780221543","wikidata":"https://www.wikidata.org/wiki/Q4681865","display_name":"Cipher","level":3,"score":0.545381486415863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5210732221603394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5085300207138062},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5046635866165161},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.43974971771240234},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.4205129146575928},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25366851687431335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2053413689136505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11015009880065918},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.08080118894577026},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00200-016-0307-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-016-0307-6","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W567095041","https://openalex.org/W584171051","https://openalex.org/W606334457","https://openalex.org/W1498993177","https://openalex.org/W1505761511","https://openalex.org/W1513703559","https://openalex.org/W1531334709","https://openalex.org/W1556443961","https://openalex.org/W1556690101","https://openalex.org/W1587687098","https://openalex.org/W1606480398","https://openalex.org/W1660562555","https://openalex.org/W1880399293","https://openalex.org/W2021094554","https://openalex.org/W2027875058","https://openalex.org/W2032685643","https://openalex.org/W2036675812","https://openalex.org/W2043694411","https://openalex.org/W2082143349","https://openalex.org/W2138047078","https://openalex.org/W2148721465","https://openalex.org/W4211127378","https://openalex.org/W4230398518","https://openalex.org/W4243205024","https://openalex.org/W4252263778","https://openalex.org/W4289126832","https://openalex.org/W4298109338"],"related_works":["https://openalex.org/W4290802965","https://openalex.org/W97789383","https://openalex.org/W3087516072","https://openalex.org/W2727156679","https://openalex.org/W2023858428","https://openalex.org/W4289406402","https://openalex.org/W2364071303","https://openalex.org/W1483053255","https://openalex.org/W2896097814","https://openalex.org/W2963940845"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
