{"id":"https://openalex.org/W2547106885","doi":"https://doi.org/10.3934/amc.2016045","title":"Computing Gr\u00f6bner bases associated with lattices","display_name":"Computing Gr\u00f6bner bases associated with lattices","publication_year":2016,"publication_date":"2016-11-01","ids":{"openalex":"https://openalex.org/W2547106885","doi":"https://doi.org/10.3934/amc.2016045","mag":"2547106885"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2016045","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016045","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=74d7f3ff-1f57-4363-bad9-385d88223dfc","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","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=74d7f3ff-1f57-4363-bad9-385d88223dfc","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026921849","display_name":"Ismara \u00c1lvarez-Barrientos","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ismara \u00c1lvarez-Barrientos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025813000","display_name":"M. Borges-Quintana","orcid":"https://orcid.org/0000-0002-5656-0037"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mijail Borges-Quintana","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018902786","display_name":"M. A. Borges-Trenard","orcid":"https://orcid.org/0000-0001-7154-7730"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miguel Angel Borges-Trenard","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017417125","display_name":"Daniel Panario","orcid":"https://orcid.org/0000-0003-3551-4063"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Panario","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026921849"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4285,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.79438419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"4","first_page":"851","last_page":"860"},"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":0.9983999729156494,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.7956943511962891},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6903355121612549},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5654355883598328},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5445911288261414},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.514330267906189},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45712465047836304},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4540945887565613},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.43199482560157776},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43025535345077515},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21699285507202148},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11083641648292542}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7956943511962891},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6903355121612549},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5654355883598328},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5445911288261414},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.514330267906189},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45712465047836304},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4540945887565613},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.43199482560157776},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43025535345077515},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21699285507202148},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11083641648292542},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/amc.2016045","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016045","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=74d7f3ff-1f57-4363-bad9-385d88223dfc","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:carleton.ca:10434","is_oa":true,"landing_page_url":"https://ir.library.carleton.ca/pub/10434","pdf_url":null,"source":{"id":"https://openalex.org/S4306402514","display_name":"Carleton University's Institutional Repository (MacOdrum Library, Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Mathematics of Communications vol. 10 no. 4, pp. 851-860","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3934/amc.2016045","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016045","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=74d7f3ff-1f57-4363-bad9-385d88223dfc","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2547106885.pdf","grobid_xml":"https://content.openalex.org/works/W2547106885.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W87785082","https://openalex.org/W1550054248","https://openalex.org/W1561016548","https://openalex.org/W2044900678","https://openalex.org/W2059522106","https://openalex.org/W2076370378","https://openalex.org/W2080336924","https://openalex.org/W2094272047","https://openalex.org/W2095573084","https://openalex.org/W2111427757","https://openalex.org/W2120641775","https://openalex.org/W2121484689","https://openalex.org/W2137439750","https://openalex.org/W2168553484","https://openalex.org/W2485296172","https://openalex.org/W2486822198","https://openalex.org/W4237780066","https://openalex.org/W4242435587"],"related_works":["https://openalex.org/W2590472383","https://openalex.org/W2383873009","https://openalex.org/W2393580911","https://openalex.org/W2212184297","https://openalex.org/W3207130397","https://openalex.org/W2046435967","https://openalex.org/W3156456913","https://openalex.org/W4231775656","https://openalex.org/W2390945180","https://openalex.org/W2394052932"],"abstract_inverted_index":{"We":[0,12],"specialize":[1],"M\u00f6ller's":[2],"algorithm":[3,25],"to":[4,10,44],"the":[5,14,33,40,45,60],"computation":[6],"ofGr\u00f6bner":[7],"bases":[8],"related":[9],"lattices.":[11,104],"give":[13],"complexityanalysis":[15],"of":[16,52,59,73,103],"our":[17,24],"algorithm.":[18],"Then":[19],"we":[20],"provide":[21],"experiments":[22],"showingthat":[23],"is":[26],"more":[27],"efficient":[28],"than":[29],"Buchberger's":[30],"algorithmfor":[31],"computing":[32],"associated":[34,43,54,76],"Gr\u00f6bner":[35],"bases.":[36],"Furthermore":[37],"weshow":[38],"that":[39,80],"binomial":[41],"ideal":[42],"lattice":[46],"can":[47],"beconstructed":[48],"from":[49],"a":[50,56,68],"set":[51,57],"binomials":[53],"with":[55,77],"ofgenerators":[58],"corresponding":[61],"label":[62,101],"code.":[63],"This":[64,84],"result":[65],"ispresented":[66],"in":[67],"general":[69],"way":[70],"by":[71],"means":[72],"three":[74],"idealconstructions":[75],"group":[78,91],"codes":[79,92,97,102],"constitute":[81],"thesame":[82],"ideal.":[83],"generalizes":[85],"earlier":[86],"results":[87],"for":[88],"specific":[89],"casesof":[90],"such":[93],"as":[94],"linear":[95],"codes,":[96],"over":[98],"${\\mathbb":[99],"Z}_m$and":[100]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}