Ontology type: schema:ScholarlyArticle
2019-08-14
AUTHORSMinjia Shi, Chenchen Wang, Rongsheng Wu, Yu Hu, Yaoqiang Chang
ABSTRACTIn this paper, a class of additive codes which is referred to as ℤ2ℤ2[u,v]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]$\end{document}-additive codes is introduced. This is a generalization towards another direction of recently introduced ℤ2ℤ4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{4}$\end{document} codes (Doughterty et al., Appl. Algebra Eng. Commun. Comput. 27(2), 123–138, 7). A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, the structure and possible weights for all one-weight and two-weight ℤ2ℤ2[u,v]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]$\end{document}-additive codes are described. Additionally, we also construct some one-weight and two-weight ℤ2ℤ2[u,v]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]$\end{document}-additive codes to illustrate our obtained results. More... »
PAGES443-454
http://scigraph.springernature.com/pub.10.1007/s12095-019-00391-5
DOIhttp://dx.doi.org/10.1007/s12095-019-00391-5
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1120333610
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT
[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
"about": [
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Applied Mathematics",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Numerical and Computational Mathematics",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China",
"id": "http://www.grid.ac/institutes/grid.252245.6",
"name": [
"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China"
],
"type": "Organization"
},
"familyName": "Shi",
"givenName": "Minjia",
"id": "sg:person.012012432235.16",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012012432235.16"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China",
"id": "http://www.grid.ac/institutes/grid.252245.6",
"name": [
"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China"
],
"type": "Organization"
},
"familyName": "Wang",
"givenName": "Chenchen",
"id": "sg:person.014240147252.79",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014240147252.79"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China",
"id": "http://www.grid.ac/institutes/grid.252245.6",
"name": [
"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China"
],
"type": "Organization"
},
"familyName": "Wu",
"givenName": "Rongsheng",
"id": "sg:person.013714562003.12",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013714562003.12"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China",
"id": "http://www.grid.ac/institutes/grid.252245.6",
"name": [
"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China"
],
"type": "Organization"
},
"familyName": "Hu",
"givenName": "Yu",
"type": "Person"
},
{
"affiliation": {
"alternateName": "Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China",
"id": "http://www.grid.ac/institutes/grid.252245.6",
"name": [
"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, 230601, Anhui, People\u2019s Republic of China"
],
"type": "Organization"
},
"familyName": "Chang",
"givenName": "Yaoqiang",
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/s10623-009-9309-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1006827122",
"https://doi.org/10.1007/s10623-009-9309-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s11424-014-2188-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1052092358",
"https://doi.org/10.1007/s11424-014-2188-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10623-007-9136-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1038465688",
"https://doi.org/10.1007/s10623-007-9136-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-57189-3_5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008575012",
"https://doi.org/10.1007/978-3-642-57189-3_5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00200-015-0273-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1006650219",
"https://doi.org/10.1007/s00200-015-0273-4"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s11424-015-3265-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044540504",
"https://doi.org/10.1007/s11424-015-3265-3"
],
"type": "CreativeWork"
}
],
"datePublished": "2019-08-14",
"datePublishedReg": "2019-08-14",
"description": "In this paper, a class of additive codes which is referred to as \u21242\u21242[u,v]\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathbb {Z}_{2}\\mathbb {Z}_{2}[u,v]$\\end{document}-additive codes is introduced. This is a generalization towards another direction of recently introduced \u21242\u21244\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathbb {Z}_{2}\\mathbb {Z}_{4}$\\end{document} codes (Doughterty et al., Appl. Algebra Eng. Commun. Comput. 27(2), 123\u2013138, 7). A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, the structure and possible weights for all one-weight and two-weight \u21242\u21242[u,v]\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathbb {Z}_{2}\\mathbb {Z}_{2}[u,v]$\\end{document}-additive codes are described. Additionally, we also construct some one-weight and two-weight \u21242\u21242[u,v]\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathbb {Z}_{2}\\mathbb {Z}_{2}[u,v]$\\end{document}-additive codes to illustrate our obtained results.",
"genre": "article",
"id": "sg:pub.10.1007/s12095-019-00391-5",
"inLanguage": "en",
"isAccessibleForFree": false,
"isFundedItemOf": [
{
"id": "sg:grant.8306127",
"type": "MonetaryGrant"
}
],
"isPartOf": [
{
"id": "sg:journal.1136695",
"issn": [
"1936-2447",
"1936-2455"
],
"name": "Cryptography and Communications",
"publisher": "Springer Nature",
"type": "Periodical"
},
{
"issueNumber": "3",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "12"
}
],
"keywords": [
"one's weight",
"weight",
"two-weight",
"results",
"class",
"enumerators",
"possible weights",
"code",
"direction",
"identity",
"additive codes",
"structure",
"MacWilliams type identities",
"weight enumerators",
"generalization",
"paper",
"dual"
],
"name": "One-weight and two-weight \u21242\u21242[u,v]-additive codes",
"pagination": "443-454",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1120333610"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s12095-019-00391-5"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s12095-019-00391-5",
"https://app.dimensions.ai/details/publication/pub.1120333610"
],
"sdDataset": "articles",
"sdDatePublished": "2022-05-20T07:35",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_791.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1007/s12095-019-00391-5"
}
]
Download the RDF metadata as: json-ld nt turtle xml License info
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s12095-019-00391-5'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s12095-019-00391-5'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12095-019-00391-5'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12095-019-00391-5'
This table displays all metadata directly associated to this object as RDF triples.
135 TRIPLES
22 PREDICATES
50 URIs
34 LITERALS
6 BLANK NODES