Codes Based on Complete Graphs View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1996-05

AUTHORS

Dieter Jungnickel, Marialuisa J. de Resmini, Scott A. Vanstone

ABSTRACT

We consider the problem of embedding the even graphicalcode based on the complete graph on n vertices intoa shortening of a Hamming code of length 2m - 1,where m=h(n) should be as small as possible. Asit turns out, this problem is equivalent to the existence problemfor optimal codes with minimum distance 5, and optimal embeddingscan 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 threeconceivable values. More... »

PAGES

159-165

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1018089026819

DOI

http://dx.doi.org/10.1023/a:1018089026819

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1001841719


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

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\u00e0di Roma ``La Sapienza'', 2, Piazzale Aldo Moro, I-00185, Roma, Italy", 
          "id": "http://www.grid.ac/institutes/None", 
          "name": [
            "Dipartimento di Matematica, Universit\u00e0di Roma ``La Sapienza'', 2, Piazzale Aldo Moro, I-00185, Roma, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Resmini", 
        "givenName": "Marialuisa J. de", 
        "id": "sg:person.012041646664.45", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012041646664.45"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Dipartimento di Matematica, Universit\u00e0di Roma ``La Sapienza'', 2, Piazzale Aldo Moro, I-00185, Roma, Italy", 
          "id": "http://www.grid.ac/institutes/None", 
          "name": [
            "Dipartimento di Matematica, Universit\u00e0di Roma ``La Sapienza'', 2, Piazzale Aldo Moro, I-00185, Roma, Italy"
          ], 
          "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": "1996-05", 
    "datePublishedReg": "1996-05-01", 
    "description": "We consider the problem of embedding the even graphicalcode based on the complete graph on n vertices intoa shortening of a Hamming code of length 2m - 1,where m=h(n) should be as small as possible. Asit turns out, this problem is equivalent to the existence problemfor optimal codes with minimum distance 5, and optimal embeddingscan 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 threeconceivable values.", 
    "genre": "article", 
    "id": "sg:pub.10.1023/a:1018089026819", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136552", 
        "issn": [
          "0925-1022", 
          "1573-7586"
        ], 
        "name": "Designs, Codes and Cryptography", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1-2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "8"
      }
    ], 
    "keywords": [
      "graphical codes", 
      "complete graph", 
      "Hamming code", 
      "optimal codes", 
      "code", 
      "graph", 
      "n vertices", 
      "form 2k", 
      "minimum distance 5", 
      "distance 5", 
      "problem", 
      "vertices", 
      "existence", 
      "Kn", 
      "possibility", 
      "values", 
      "length", 
      "consequences"
    ], 
    "name": "Codes Based on Complete Graphs", 
    "pagination": "159-165", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1001841719"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1023/a:1018089026819"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1023/a:1018089026819", 
      "https://app.dimensions.ai/details/publication/pub.1001841719"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-09-02T15:49", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/article/article_299.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1023/a:1018089026819"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

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.10.1023/a:1018089026819'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1018089026819'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1018089026819'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1018089026819'


 

This table displays all metadata directly associated to this object as RDF triples.

92 TRIPLES      20 PREDICATES      43 URIs      35 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1023/a:1018089026819 schema:about anzsrc-for:08
2 anzsrc-for:0804
3 schema:author Ndb297fa8740b4dae8aec789c5b3f1cda
4 schema:datePublished 1996-05
5 schema:datePublishedReg 1996-05-01
6 schema:description We consider the problem of embedding the even graphicalcode based on the complete graph on n vertices intoa shortening of a Hamming code of length 2m - 1,where m=h(n) should be as small as possible. Asit turns out, this problem is equivalent to the existence problemfor optimal codes with minimum distance 5, and optimal embeddingscan 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 threeconceivable values.
7 schema:genre article
8 schema:isAccessibleForFree false
9 schema:isPartOf N7d462c2114f34c1f9d36a7d612fe0234
10 Ne7c820cde89b4e2da8d4358e58c120c8
11 sg:journal.1136552
12 schema:keywords Hamming code
13 Kn
14 code
15 complete graph
16 consequences
17 distance 5
18 existence
19 form 2k
20 graph
21 graphical codes
22 length
23 minimum distance 5
24 n vertices
25 optimal codes
26 possibility
27 problem
28 values
29 vertices
30 schema:name Codes Based on Complete Graphs
31 schema:pagination 159-165
32 schema:productId N3d28d0e631f24e7c9e833d6be76d359f
33 Nc76c6a874caf494f906441f8ef360c24
34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001841719
35 https://doi.org/10.1023/a:1018089026819
36 schema:sdDatePublished 2022-09-02T15:49
37 schema:sdLicense https://scigraph.springernature.com/explorer/license/
38 schema:sdPublisher N59550631bfbc4cf6a5af4d017003f670
39 schema:url https://doi.org/10.1023/a:1018089026819
40 sgo:license sg:explorer/license/
41 sgo:sdDataset articles
42 rdf:type schema:ScholarlyArticle
43 N3d28d0e631f24e7c9e833d6be76d359f schema:name dimensions_id
44 schema:value pub.1001841719
45 rdf:type schema:PropertyValue
46 N44dfaa77e8bc42ce8fe57f50ed86bf6e rdf:first sg:person.010344544767.07
47 rdf:rest rdf:nil
48 N4ba01272292e4defb099b2769fc92664 rdf:first sg:person.012041646664.45
49 rdf:rest N44dfaa77e8bc42ce8fe57f50ed86bf6e
50 N59550631bfbc4cf6a5af4d017003f670 schema:name Springer Nature - SN SciGraph project
51 rdf:type schema:Organization
52 N7d462c2114f34c1f9d36a7d612fe0234 schema:volumeNumber 8
53 rdf:type schema:PublicationVolume
54 Nc76c6a874caf494f906441f8ef360c24 schema:name doi
55 schema:value 10.1023/a:1018089026819
56 rdf:type schema:PropertyValue
57 Ndb297fa8740b4dae8aec789c5b3f1cda rdf:first sg:person.016273474670.91
58 rdf:rest N4ba01272292e4defb099b2769fc92664
59 Ne7c820cde89b4e2da8d4358e58c120c8 schema:issueNumber 1-2
60 rdf:type schema:PublicationIssue
61 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
62 schema:name Information and Computing Sciences
63 rdf:type schema:DefinedTerm
64 anzsrc-for:0804 schema:inDefinedTermSet anzsrc-for:
65 schema:name Data Format
66 rdf:type schema:DefinedTerm
67 sg:journal.1136552 schema:issn 0925-1022
68 1573-7586
69 schema:name Designs, Codes and Cryptography
70 schema:publisher Springer Nature
71 rdf:type schema:Periodical
72 sg:person.010344544767.07 schema:affiliation grid-institutes:None
73 schema:familyName Vanstone
74 schema:givenName Scott A.
75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07
76 rdf:type schema:Person
77 sg:person.012041646664.45 schema:affiliation grid-institutes:None
78 schema:familyName Resmini
79 schema:givenName Marialuisa J. de
80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012041646664.45
81 rdf:type schema:Person
82 sg:person.016273474670.91 schema:affiliation grid-institutes:grid.7307.3
83 schema:familyName Jungnickel
84 schema:givenName Dieter
85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016273474670.91
86 rdf:type schema:Person
87 grid-institutes:None schema:alternateName Dipartimento di Matematica, Universitàdi Roma ``La Sapienza'', 2, Piazzale Aldo Moro, I-00185, Roma, Italy
88 schema:name Dipartimento di Matematica, Universitàdi Roma ``La Sapienza'', 2, Piazzale Aldo Moro, I-00185, Roma, Italy
89 rdf:type schema:Organization
90 grid-institutes:grid.7307.3 schema:alternateName Lehrstuhl für Angewandte Mathematik II, Universität Augsburg, D-86135, Augsburg, Germany
91 schema:name Lehrstuhl für Angewandte Mathematik II, Universität Augsburg, D-86135, Augsburg, Germany
92 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...