{"id":"https://openalex.org/W2588528202","doi":"https://doi.org/10.1109/allerton.2016.7852318","title":"Quasi-Quadratic Residue Codes and their weight distributions","display_name":"Quasi-Quadratic Residue Codes and their weight distributions","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2588528202","doi":"https://doi.org/10.1109/allerton.2016.7852318","mag":"2588528202"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2016.7852318","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2016.7852318","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5069834567","display_name":"Nigel Boston","orcid":"https://orcid.org/0000-0002-2807-4963"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nigel Boston","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, WI, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, WI, United States","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087248118","display_name":"Jing Hao","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jing Hao","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, WI, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, WI, United States","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":null,"first_page":"822","last_page":"829"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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":0.9994999766349792,"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/T14281","display_name":"Islamic Finance and Communication","score":0.9629999995231628,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7118521928787231},{"id":"https://openalex.org/keywords/quadratic-residue","display_name":"Quadratic residue","score":0.6340758800506592},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.541344404220581},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5406062602996826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5203306674957275},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.512603223323822},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.4921962320804596},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.47453463077545166},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4688993990421295},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4511430263519287},{"id":"https://openalex.org/keywords/residue","display_name":"Residue (chemistry)","score":0.42018434405326843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27162134647369385},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09003770351409912}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7118521928787231},{"id":"https://openalex.org/C12817185","wikidata":"https://www.wikidata.org/wiki/Q878259","display_name":"Quadratic residue","level":2,"score":0.6340758800506592},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.541344404220581},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5406062602996826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5203306674957275},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.512603223323822},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.4921962320804596},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.47453463077545166},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4688993990421295},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4511430263519287},{"id":"https://openalex.org/C2781338088","wikidata":"https://www.wikidata.org/wiki/Q903495","display_name":"Residue (chemistry)","level":2,"score":0.42018434405326843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27162134647369385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09003770351409912},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton.2016.7852318","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2016.7852318","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W618390265","https://openalex.org/W1606480398","https://openalex.org/W1810090164","https://openalex.org/W1967377547","https://openalex.org/W1984686096","https://openalex.org/W2014944833","https://openalex.org/W2025528403","https://openalex.org/W2119048459","https://openalex.org/W2126377499","https://openalex.org/W2171478552","https://openalex.org/W4255297036","https://openalex.org/W6638417059","https://openalex.org/W6641932603"],"related_works":["https://openalex.org/W1996305421","https://openalex.org/W2380806311","https://openalex.org/W4300517272","https://openalex.org/W2963553930","https://openalex.org/W4289596368","https://openalex.org/W4302155387","https://openalex.org/W2545189445","https://openalex.org/W2115024785","https://openalex.org/W2085781584","https://openalex.org/W4392635288"],"abstract_inverted_index":{"Quasi-Quadratic":[0],"Residue":[1],"Codes":[2,95],"(QQR":[3],"Codes)":[4],"are":[5,13],"a":[6,34,45,66,69,115,190],"family":[7],"of":[8,60,71,78,80,114,162,166,192],"double":[9],"circulant":[10],"codes.":[11],"They":[12],"important":[14],"in":[15],"at":[16,119],"least":[17,120],"two":[18],"respects:":[19],"Firstly,":[20],"they":[21,42,197],"have":[22],"very":[23],"good":[24],"minimum":[25,141],"distances":[26],"when":[27,104],"p":[28,105,152],"\u2261":[29,106],"3":[30],"(mod":[31,108,154],"8),":[32,155],"providing":[33],"critical":[35],"test":[36],"case":[37],"for":[38,48],"Goppa's":[39],"Conjecture.":[40],"Secondly,":[41],"serve":[43],"as":[44],"powerful":[46],"tool":[47],"studying":[49],"point":[50],"distributions":[51,63],"on":[52,68,74,82,93,181],"hyperelliptic":[53,83],"curves.":[54,84],"We":[55,99,143,187],"will":[56,89,100],"use":[57],"the":[58,111,158,163,167,177,199],"result":[59,70],"their":[61,149],"weight":[62,112,160],"to":[64],"prove":[65,103],"variant":[67],"Larsen":[72],"[1]":[73],"asymptotic":[75],"normal":[76],"distribution":[77],"numbers":[79],"points":[81],"In":[85],"this":[86],"paper,":[87],"we":[88],"show":[90],"new":[91,146],"results":[92,147],"QQR":[94,116],"from":[96],"several":[97],"perspectives.":[98],"observe":[101],"(and":[102],"7":[107,153],"8))":[109],"that":[110],"polynomial":[113],"Code":[117],"is":[118,139,157],"divisible":[121],"by":[122],"(x":[123],"<sup":[124,129,133],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[125,130,134,184],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[126,131],"+":[127],"y":[128],")":[132],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d-1</sup>":[135],",":[136],"where":[137],"d":[138],"its":[140],"distance.":[142],"also":[144,188],"provide":[145],"about":[148],"structures.":[150],"When":[151],"it":[156],"even":[159],"subcode":[161],"direct":[164],"sum":[165],"quadratic":[168],"residue":[169],"code":[170],"with":[171],"itself.":[172],"Its":[173],"automorphism":[174],"group":[175],"contains":[176],"invertible":[178],"affine":[179],"transformations":[180],"F":[182],"<sub":[183],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[185],".":[186],"answer":[189],"question":[191],"Joyner":[193],"[2]":[194],"asking":[195],"whether":[196],"satisfy":[198],"Riemann":[200],"hypothesis.":[201]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}