Ontology type: schema:ScholarlyArticle
2012-07
AUTHORSE. Couselo, S. González, V. T. Markov, C. Martínez, A. A. Nechaev
ABSTRACTReed–Solomon codes and Reed–Muller codes are represented as ideals of the group ring S = QH of an elementary Abelian p-group H over a finite field Q = of characteristic p. Such representations for these codes are already known. Our technique differs from the previously used method in the following. There, the codes in question were represented as kernels of some homomorphisms; in other words, these were defined by some kind of parity-check relations. Here, we explicitly specify generators for the ideals presenting the codes. In this case Reed–Muller codes are obtained by applying the trace function to some sums of one-dimensional subspaces of QS in a fixed set of q such subspaces, whose sums also present Reed–Solomon codes. More... »
PAGES195-212
http://scigraph.springernature.com/pub.10.1007/s10469-012-9183-8
DOIhttp://dx.doi.org/10.1007/s10469-012-9183-8
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1037147809
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/2008/2002",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Cultural Studies",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/20",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Language, Communication and Culture",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "University of Oviedo",
"id": "https://www.grid.ac/institutes/grid.10863.3c",
"name": [
"University of Oviedo, Calvo Sotelo s/n, 33007, Oviedo, Spain"
],
"type": "Organization"
},
"familyName": "Couselo",
"givenName": "E.",
"id": "sg:person.015442547225.50",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015442547225.50"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "University of Oviedo",
"id": "https://www.grid.ac/institutes/grid.10863.3c",
"name": [
"University of Oviedo, Calvo Sotelo s/n, 33007, Oviedo, Spain"
],
"type": "Organization"
},
"familyName": "Gonz\u00e1lez",
"givenName": "S.",
"id": "sg:person.016661036521.95",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016661036521.95"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Moscow State University",
"id": "https://www.grid.ac/institutes/grid.14476.30",
"name": [
"Moscow State University, Moscow, Russia"
],
"type": "Organization"
},
"familyName": "Markov",
"givenName": "V. T.",
"id": "sg:person.013530345023.45",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013530345023.45"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "University of Oviedo",
"id": "https://www.grid.ac/institutes/grid.10863.3c",
"name": [
"University of Oviedo, Calvo Sotelo s/n, 33007, Oviedo, Spain"
],
"type": "Organization"
},
"familyName": "Mart\u00ednez",
"givenName": "C.",
"id": "sg:person.015261576461.61",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015261576461.61"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Moscow State University",
"id": "https://www.grid.ac/institutes/grid.14476.30",
"name": [
"Moscow State University, Moscow, Russia"
],
"type": "Organization"
},
"familyName": "Nechaev",
"givenName": "A. A.",
"id": "sg:person.016564362223.63",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016564362223.63"
],
"type": "Person"
}
],
"citation": [
{
"id": "https://doi.org/10.1016/j.laa.2010.03.002",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1010355195"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00141972",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026374935",
"https://doi.org/10.1007/bf00141972"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00141972",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026374935",
"https://doi.org/10.1007/bf00141972"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1028360868",
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-78659-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1028360868",
"https://doi.org/10.1007/978-3-642-78659-4"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-78659-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1028360868",
"https://doi.org/10.1007/978-3-642-78659-4"
],
"type": "CreativeWork"
}
],
"datePublished": "2012-07",
"datePublishedReg": "2012-07-01",
"description": "Reed\u2013Solomon codes and Reed\u2013Muller codes are represented as ideals of the group ring S = QH of an elementary Abelian p-group H over a finite field Q = of characteristic p. Such representations for these codes are already known. Our technique differs from the previously used method in the following. There, the codes in question were represented as kernels of some homomorphisms; in other words, these were defined by some kind of parity-check relations. Here, we explicitly specify generators for the ideals presenting the codes. In this case Reed\u2013Muller codes are obtained by applying the trace function to some sums of one-dimensional subspaces of QS in a fixed set of q such subspaces, whose sums also present Reed\u2013Solomon codes.",
"genre": "research_article",
"id": "sg:pub.10.1007/s10469-012-9183-8",
"inLanguage": [
"en"
],
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1136408",
"issn": [
"0002-5232",
"1573-8302"
],
"name": "Algebra and Logic",
"type": "Periodical"
},
{
"issueNumber": "3",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "51"
}
],
"name": "Ideal representation of Reed\u2013Solomon and Reed\u2013Muller codes",
"pagination": "195-212",
"productId": [
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"b0f5cd1f9aa87a06399d237709c40b30043676634beaf03da569ed7d70731902"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s10469-012-9183-8"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1037147809"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s10469-012-9183-8",
"https://app.dimensions.ai/details/publication/pub.1037147809"
],
"sdDataset": "articles",
"sdDatePublished": "2019-04-10T16:43",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8669_00000514.jsonl",
"type": "ScholarlyArticle",
"url": "http://link.springer.com/10.1007%2Fs10469-012-9183-8"
}
]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/s10469-012-9183-8'
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/s10469-012-9183-8'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10469-012-9183-8'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10469-012-9183-8'
This table displays all metadata directly associated to this object as RDF triples.
105 TRIPLES
21 PREDICATES
31 URIs
19 LITERALS
7 BLANK NODES