1996
AUTHORSDieter Jungnickel , Marialuisa J. De Resmini , Scott A. Vanstone
ABSTRACTWe consider the problem of embedding the even graphical code based on the complete graph on n vertices into a shortening of a Hamming code of length 2m - 1, where m = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based on Kn. As a consequence, we are able to determine h(n) exactly for all n of the form 2k + 1 and to narrow down the possibilities in general to two or three conceivable values. More... »
PAGES159-165
Designs and Finite Geometries
ISBN
978-1-4612-8604-2
978-1-4613-1395-3
http://scigraph.springernature.com/pub.10.1007/978-1-4613-1395-3_11
DOIhttp://dx.doi.org/10.1007/978-1-4613-1395-3_11
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1021658850
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/2008/08",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Information and Computing Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0804",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Data Format",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Lehrstuhl f\u00fcr Angewandte Mathematik II, Universit\u00e4t Augsburg, D-86135, Augsburg, Germany",
"id": "http://www.grid.ac/institutes/grid.7307.3",
"name": [
"Lehrstuhl f\u00fcr Angewandte Mathematik II, Universit\u00e4t Augsburg, D-86135, Augsburg, Germany"
],
"type": "Organization"
},
"familyName": "Jungnickel",
"givenName": "Dieter",
"id": "sg:person.016273474670.91",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016273474670.91"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Dipartimento di Matematica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, 2, Piazzale Aldo Moro, I-00185, Roma, Italy",
"id": "http://www.grid.ac/institutes/grid.7841.a",
"name": [
"Dipartimento di Matematica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, 2, Piazzale Aldo Moro, I-00185, Roma, Italy"
],
"type": "Organization"
},
"familyName": "De Resmini",
"givenName": "Marialuisa J.",
"id": "sg:person.012712302064.14",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012712302064.14"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Dept. of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada",
"id": "http://www.grid.ac/institutes/grid.46078.3d",
"name": [
"Dept. of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada"
],
"type": "Organization"
},
"familyName": "Vanstone",
"givenName": "Scott A.",
"id": "sg:person.010344544767.07",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07"
],
"type": "Person"
}
],
"datePublished": "1996",
"datePublishedReg": "1996-01-01",
"description": "We consider the problem of embedding the even graphical code based on the complete graph on n vertices into a shortening of a Hamming code of length 2m - 1, where m = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based on Kn. As a consequence, we are able to determine h(n) exactly for all n of the form 2k + 1 and to narrow down the possibilities in general to two or three conceivable values.",
"editor": [
{
"familyName": "Jungnickel",
"givenName": "Dieter",
"type": "Person"
}
],
"genre": "chapter",
"id": "sg:pub.10.1007/978-1-4613-1395-3_11",
"isAccessibleForFree": false,
"isPartOf": {
"isbn": [
"978-1-4612-8604-2",
"978-1-4613-1395-3"
],
"name": "Designs and Finite Geometries",
"type": "Book"
},
"keywords": [
"graphical codes",
"Hamming code",
"optimal codes",
"optimal embedding",
"code",
"complete graph",
"graph",
"embedding",
"n vertices",
"existence problem",
"vertices",
"form 2k",
"conceivable values",
"distance 5",
"minimum distance 5",
"possibility",
"values",
"consequences",
"length",
"Kn",
"problem",
"shortening"
],
"name": "Codes Based on Complete Graphs",
"pagination": "159-165",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1021658850"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-1-4613-1395-3_11"
]
}
],
"publisher": {
"name": "Springer Nature",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-1-4613-1395-3_11",
"https://app.dimensions.ai/details/publication/pub.1021658850"
],
"sdDataset": "chapters",
"sdDatePublished": "2022-08-04T17:16",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220804/entities/gbq_results/chapter/chapter_242.jsonl",
"type": "Chapter",
"url": "https://doi.org/10.1007/978-1-4613-1395-3_11"
}
]
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.10.1007/978-1-4613-1395-3_11'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4613-1395-3_11'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4613-1395-3_11'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4613-1395-3_11'
This table displays all metadata directly associated to this object as RDF triples.
101 TRIPLES
22 PREDICATES
47 URIs
40 LITERALS
7 BLANK NODES