{"id":"https://openalex.org/W2074822772","doi":"https://doi.org/10.1109/itwitwn.2007.4318055","title":"Actions of the Unitary Group on Irreducible/Primitive Polynomials and Their Applications to Randomness of Sequences","display_name":"Actions of the Unitary Group on Irreducible/Primitive Polynomials and Their Applications to Randomness of Sequences","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2074822772","doi":"https://doi.org/10.1109/itwitwn.2007.4318055","mag":"2074822772"},"language":"en","primary_location":{"id":"doi:10.1109/itwitwn.2007.4318055","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itwitwn.2007.4318055","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks","raw_type":"proceedings-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/A5109178350","display_name":"Solomon W. Golomb","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Solomon W. Golomb","raw_affiliation_strings":["Department of EF_SYSTEMS, University of Southern California, Los Angeles, CA, USA","University of Southern California , Los Angeles#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of EF_SYSTEMS, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"University of Southern California , Los Angeles#TAB#","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036636567","display_name":"Guang Gong","orcid":"https://orcid.org/0000-0003-2684-9259"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Guang Gong","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ONT, Canada","Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, CANADA, Email. ggong@calliope.uwaterloo.ca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ONT, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, CANADA, Email. ggong@calliope.uwaterloo.ca","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4844,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75925347,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/randomness","display_name":"Randomness","score":0.7541695833206177},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.7357702851295471},{"id":"https://openalex.org/keywords/irreducibility","display_name":"Irreducibility","score":0.7030673027038574},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6339125633239746},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5329272150993347},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4364498555660248},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40798696875572205},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35217568278312683},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.332761287689209},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08063599467277527},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06891041994094849}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.7541695833206177},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7357702851295471},{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.7030673027038574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6339125633239746},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5329272150993347},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4364498555660248},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40798696875572205},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35217568278312683},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.332761287689209},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08063599467277527},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06891041994094849},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itwitwn.2007.4318055","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itwitwn.2007.4318055","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1984377013","https://openalex.org/W2116256818","https://openalex.org/W2157294036","https://openalex.org/W2161972985","https://openalex.org/W4243205024"],"related_works":["https://openalex.org/W1630580488","https://openalex.org/W2007170860","https://openalex.org/W4319349750","https://openalex.org/W2951407429","https://openalex.org/W4246385323","https://openalex.org/W2145139444","https://openalex.org/W4383993686","https://openalex.org/W4379981171","https://openalex.org/W2951751533","https://openalex.org/W1975578379"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"how":[3],"irreducibility":[4],"and":[5,25],"primitivity":[6],"can":[7],"be":[8],"preserved":[9],"when":[10],"the":[11,30],"unitary":[12],"group":[13],"acts":[14],"on":[15],"irreducible":[16],"or":[17],"primitive":[18],"polynomials.":[19],"Applying":[20],"these":[21,45],"operators":[22],"to":[23],"sequences":[24,55],"their":[26],"discrete":[27],"Fourier":[28],"spectra,":[29],"weight":[31],"preserving":[32],"property":[33],"is":[34],"obtained.":[35],"Some":[36],"new":[37],"randomness":[38],"criteria":[39],"are":[40,48],"introduced":[41],"in":[42,57],"terms":[43],"of":[44,53],"operators,":[46],"which":[47],"suitable":[49],"for":[50],"measuring":[51],"unpredictibility":[52],"pseudo-random":[54],"employed":[56],"stream":[58],"ciphers.":[59]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
