{"id":"https://openalex.org/W2991692345","doi":"https://doi.org/10.37236/1228","title":"On a Class of Constant Weight Codes","display_name":"On a Class of Constant Weight Codes","publication_year":1996,"publication_date":"1996-01-02","ids":{"openalex":"https://openalex.org/W2991692345","doi":"https://doi.org/10.37236/1228","mag":"2991692345"},"language":"en","primary_location":{"id":"doi:10.37236/1228","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1228","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r4/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r4/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091589229","display_name":"Mihai Caragiu","orcid":"https://orcid.org/0000-0003-2639-6683"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mihai Caragiu","raw_affiliation_strings":["Institute of Mathematics Bucharest and Department of Mathematics, Pennsylvania State University"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics Bucharest and Department of Mathematics, Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091589229"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":1.1045,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84947487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":"1","first_page":null,"last_page":null},"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":0.9987000226974487,"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":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.8597986698150635},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7584846019744873},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.7537733316421509},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.6649817228317261},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.6280564069747925},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.5522333979606628},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5069361329078674},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.48817068338394165},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4797471761703491},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.47240275144577026},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.46558111906051636},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.42738038301467896},{"id":"https://openalex.org/keywords/quadratic-residue","display_name":"Quadratic residue","score":0.41317468881607056},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.3649134933948517},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.18827295303344727},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07558631896972656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8597986698150635},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7584846019744873},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.7537733316421509},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.6649817228317261},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.6280564069747925},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.5522333979606628},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5069361329078674},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.48817068338394165},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4797471761703491},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.47240275144577026},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.46558111906051636},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.42738038301467896},{"id":"https://openalex.org/C12817185","wikidata":"https://www.wikidata.org/wiki/Q878259","display_name":"Quadratic residue","level":2,"score":0.41317468881607056},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3649134933948517},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.18827295303344727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07558631896972656},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1228","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1228","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r4/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1228","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1228","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r4/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2991692345.pdf","grobid_xml":"https://content.openalex.org/works/W2991692345.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W656708819","https://openalex.org/W1489774662","https://openalex.org/W1512395286","https://openalex.org/W1557415002","https://openalex.org/W1583607006","https://openalex.org/W1606480398","https://openalex.org/W1966394702","https://openalex.org/W2031193265","https://openalex.org/W2147067885","https://openalex.org/W2151436648","https://openalex.org/W2160519701","https://openalex.org/W2165855190","https://openalex.org/W2732251371","https://openalex.org/W3144798926","https://openalex.org/W4302035717"],"related_works":["https://openalex.org/W2591781490","https://openalex.org/W4301387403","https://openalex.org/W1794215636","https://openalex.org/W2039764764","https://openalex.org/W2963238462","https://openalex.org/W2794456507","https://openalex.org/W2963553930","https://openalex.org/W1680404258","https://openalex.org/W2008585918","https://openalex.org/W2991692345"],"abstract_inverted_index":{"For":[0],"any":[1,31],"odd":[2],"prime":[3],"power":[4],"$q$":[5,20,77],"we":[6,48,65,98,133],"first":[7],"construct":[8],"a":[9],"certain":[10],"non-linear":[11],"binary":[12,70],"code":[13],"$C(q,2)$":[14,51],"having":[15],"$(q^2-q)/2$":[16],"codewords":[17,34,132],"of":[18,69,75,102,110,148,154,162,172],"length":[19,76],"and":[21,56,83,85,90,128,169],"weight":[22],"$(q-1)/2$":[23],"each,":[24],"for":[25,87],"which":[26,151],"the":[27,37,100,108,124,131,144,152,160,163,170,173],"Hamming":[28],"distance":[29],"between":[30],"two":[32],"distinct":[33],"is":[35,52,121,135,156],"in":[36,130,150],"range":[38,153],"$[q/2-3\\sqrt":[39],"q/2,\\":[40],"q/2+3\\sqrt":[41],"q/2]$":[42],"that":[43,50,78,123],"is,":[44],"'almost":[45,80],"constant'.":[46],"Moreover,":[47],"prove":[49,99],"distance-invariant.":[53],"Several":[54],"variations":[55],"improvements":[57],"on":[58,117],"this":[59],"theme":[60],"are":[61,176],"then":[62],"pursued.":[63],"Thus,":[64],"produce":[66],"other":[67],"classes":[68],"codes":[71,105,168,175],"$C(q,n)$,":[72],"$n\\geq":[73],"3$,":[74],"have":[79,93],"constant'":[81],"weights":[82],"distances,":[84],"which,":[86],"fixed":[88],"$n$":[89],"big":[91],"$q$,":[92],"asymptotically":[94],"$q^n/n$":[95],"codewords.":[96,112],"Then":[97],"possibility":[101],"extending":[103],"our":[104],"by":[106,114],"adding":[107],"complements":[109],"their":[111],"Also,":[113],"using":[115],"results":[116],"Artin":[118],"$L-$series,":[119],"it":[120],"shown":[122],"distribution":[125],"ofthe":[126],"$0$'s":[127],"$1$'s":[129],"constructed":[134],"quasi-random.":[136],"Our":[137],"construction":[138],"uses":[139],"character":[140,146],"sums":[141],"associated":[142],"with":[143,159],"quadratic":[145],"$\\chi$":[147],"$F_{q^n}$":[149],"summation":[155],"$F_q$.":[157],"Relations":[158],"duals":[161,171],"double":[164],"error":[165],"correcting":[166],"BCH":[167],"Melas":[174],"also":[177],"discussed.":[178]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
