{"id":"https://openalex.org/W2470534783","doi":"https://doi.org/10.1007/s00200-017-0344-9","title":"How to obtain lattices from $$(f,\\sigma ,\\delta )$$ ( f , \u03c3 , \u03b4 ) -codes via a generalization of Construction A","display_name":"How to obtain lattices from $$(f,\\sigma ,\\delta )$$ ( f , \u03c3 , \u03b4 ) -codes via a generalization of Construction A","publication_year":2017,"publication_date":"2017-10-16","ids":{"openalex":"https://openalex.org/W2470534783","doi":"https://doi.org/10.1007/s00200-017-0344-9","mag":"2470534783"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-017-0344-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-017-0344-9","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00200-017-0344-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00200-017-0344-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109998506","display_name":"S. Pumpl\u00fcn","orcid":null},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"S. Pumpl\u00fcn","raw_affiliation_strings":["School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109998506"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.8306,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.79453662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"29","issue":"4","first_page":"313","last_page":"333"},"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":0.9995999932289124,"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/T10849","display_name":"Finite Group Theory Research","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.7961193323135376},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.7281023263931274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6161694526672363},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5398314595222473},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5350291728973389},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5131848454475403},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5126739740371704},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5058915019035339},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.4740431308746338},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43417122960090637},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4303682744503021},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41130346059799194},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37799394130706787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17219087481498718},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08300146460533142},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06675657629966736}],"concepts":[{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.7961193323135376},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7281023263931274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6161694526672363},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5398314595222473},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5350291728973389},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5131848454475403},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5126739740371704},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5058915019035339},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.4740431308746338},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43417122960090637},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4303682744503021},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41130346059799194},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37799394130706787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17219087481498718},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08300146460533142},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06675657629966736},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00200-017-0344-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-017-0344-9","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00200-017-0344-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.03787","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.03787","pdf_url":"https://arxiv.org/pdf/1607.03787","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:eprints.nottingham.ac.uk:46898","is_oa":true,"landing_page_url":"http://eprints.nottingham.ac.uk/46898/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402013","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:2461434","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/2461434","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:nottingham-repository.worktribe.com:948786","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/948786","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00200-017-0344-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-017-0344-9","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00200-017-0344-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320324","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2470534783.pdf","grobid_xml":"https://content.openalex.org/works/W2470534783.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W147781612","https://openalex.org/W165259598","https://openalex.org/W180233073","https://openalex.org/W643441626","https://openalex.org/W762550807","https://openalex.org/W1516573753","https://openalex.org/W1520389133","https://openalex.org/W1554315206","https://openalex.org/W1583847540","https://openalex.org/W1682915564","https://openalex.org/W1808382989","https://openalex.org/W1933541267","https://openalex.org/W1964702022","https://openalex.org/W1991869485","https://openalex.org/W1995990042","https://openalex.org/W2013802129","https://openalex.org/W2016652749","https://openalex.org/W2017765048","https://openalex.org/W2026879025","https://openalex.org/W2027857412","https://openalex.org/W2037199549","https://openalex.org/W2044689213","https://openalex.org/W2051677450","https://openalex.org/W2055847390","https://openalex.org/W2058787114","https://openalex.org/W2061315961","https://openalex.org/W2065359399","https://openalex.org/W2066114766","https://openalex.org/W2069738583","https://openalex.org/W2076526768","https://openalex.org/W2094267119","https://openalex.org/W2108964585","https://openalex.org/W2120165391","https://openalex.org/W2131517359","https://openalex.org/W2131764879","https://openalex.org/W2133384197","https://openalex.org/W2139489359","https://openalex.org/W2151359594","https://openalex.org/W2167697875","https://openalex.org/W2191173080","https://openalex.org/W2255958584","https://openalex.org/W2256612398","https://openalex.org/W2286490152","https://openalex.org/W2295827263","https://openalex.org/W2296020509","https://openalex.org/W2313696386","https://openalex.org/W2319357121","https://openalex.org/W2322629821","https://openalex.org/W2331005958","https://openalex.org/W2332502425","https://openalex.org/W2392371348","https://openalex.org/W2402718152","https://openalex.org/W2564904141","https://openalex.org/W2578442400","https://openalex.org/W2589009567","https://openalex.org/W2608395580","https://openalex.org/W2963519039","https://openalex.org/W2964271101","https://openalex.org/W3100512198","https://openalex.org/W3101798211","https://openalex.org/W3209191360","https://openalex.org/W4230413036","https://openalex.org/W4247118133","https://openalex.org/W4250950881","https://openalex.org/W4292408570"],"related_works":["https://openalex.org/W1123825931","https://openalex.org/W1576049389","https://openalex.org/W4288570797","https://openalex.org/W1974287725","https://openalex.org/W4295253537","https://openalex.org/W1723526129","https://openalex.org/W2795912694","https://openalex.org/W2063752695","https://openalex.org/W2059672880","https://openalex.org/W2146163384"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"cyclic":[3],"$$(f,\\sigma":[4],",\\delta":[5],")$$":[6],"-codes":[7],"over":[8],"finite":[9],"rings":[10],"canonically":[11],"induce":[12],"a":[13,69],"$${\\mathbb":[14,18],"{Z}}$$":[15],"-lattice":[16],"in":[17,26,56,91],"{R}}^N$$":[19],"by":[20,47,62,98],"using":[21,31,41],"certain":[22,42],"quotients":[23,53],"of":[24,54,71],"orders":[25,55],"nonassociative":[27],"division":[28,59],"algebras":[29,60],"defined":[30,61],"the":[32,39,72,83],"skew":[33],"polynomial":[34],"f.":[35],"This":[36],"construction":[37],"generalizes":[38],"one":[40],"$$\\sigma":[43],"$$":[44],"-constacyclic":[45],"codes":[46],"Ducoat":[48,99],"and":[49,64,100],"Oggier,":[50],"which":[51],"used":[52],"non-commutative":[57],"associative":[58],"f,":[63],"can":[65],"be":[66,86],"viewed":[67],"as":[68,104],"generalization":[70],"classical":[73],"Construction":[74],"A":[75],"for":[76],"lattices":[77],"from":[78],"linear":[79],"codes.":[80],"It":[81],"has":[82],"potential":[84],"to":[85,88,93],"applied":[87],"coset":[89],"coding,":[90],"particular":[92],"wire-tap":[94],"coding.":[95],"Previous":[96],"results":[97],"Oggier":[101],"are":[102],"obtained":[103],"special":[105],"cases.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2016-07-22T00:00:00"}