On the dimension of an APN code View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2011-12

AUTHORS

John F. Dillon

ABSTRACT

A map f : V: = GF(2m) → V is APN (almost perfect nonlinear) if its directional derivatives in nonzero directions are all 2-to-1. If m is greater than 2 and f vanishes at 0, then this derivative condition is equivalent to the condition that the binary linear code of length 2m − 1, whose parity check matrix has jth column equal to , is double-error-correcting, where ω is primitive in V. Carlet et al. (Designs Codes Cryptogr 15:125–156, 1998) proved that this code has dimension 2m − 1 − 2m; but their indirect proof uses a subtle argument involving general code parameter bounds to show that a double-error correcting code of this length could not be larger. We show here that this result follows immediately from a well-known result on bent functions ...a subject dear to the heart of Jacques Wolfmann. More... »

PAGES

275

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12095-011-0049-z

DOI

http://dx.doi.org/10.1007/s12095-011-0049-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1050580250


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/2008/0804", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Data Format", 
        "type": "DefinedTerm"
      }, 
      {
        "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"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "National Security Agency", 
          "id": "https://www.grid.ac/institutes/grid.482831.4", 
          "name": [
            "National Security Agency, 20755, Fort George G. Meade, MD, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Dillon", 
        "givenName": "John F.", 
        "id": "sg:person.016635145707.14", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016635145707.14"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1023/a:1008344232130", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027536103", 
          "https://doi.org/10.1023/a:1008344232130"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2011-12", 
    "datePublishedReg": "2011-12-01", 
    "description": "A map f : V: = GF(2m) \u2192 V is APN (almost perfect nonlinear) if its directional derivatives in nonzero directions are all 2-to-1. If m is greater than 2 and f vanishes at 0, then this derivative condition is equivalent to the condition that the binary linear code of length 2m \u2212 1, whose parity check matrix has jth column equal to , is double-error-correcting, where \u03c9 is primitive in V. Carlet et al. (Designs Codes Cryptogr 15:125\u2013156, 1998) proved that this code has dimension 2m \u2212 1 \u2212 2m; but their indirect proof uses a subtle argument involving general code parameter bounds to show that a double-error correcting code of this length could not be larger. We show here that this result follows immediately from a well-known result on bent functions ...a subject dear to the heart of Jacques Wolfmann.", 
    "genre": "non_research_article", 
    "id": "sg:pub.10.1007/s12095-011-0049-z", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136695", 
        "issn": [
          "1936-2447", 
          "1936-2455"
        ], 
        "name": "Cryptography and Communications", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "3"
      }
    ], 
    "name": "On the dimension of an APN code", 
    "pagination": "275", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "f0f2640de8ad107652f11f031bc0f3aa952a9729218158f62a503603f8dec309"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s12095-011-0049-z"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1050580250"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s12095-011-0049-z", 
      "https://app.dimensions.ai/details/publication/pub.1050580250"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T21:39", 
    "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_8687_00000524.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs12095-011-0049-z"
  }
]
 

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.10.1007/s12095-011-0049-z'

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/s12095-011-0049-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12095-011-0049-z'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12095-011-0049-z'


 

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

65 TRIPLES      21 PREDICATES      28 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s12095-011-0049-z schema:about anzsrc-for:08
2 anzsrc-for:0804
3 schema:author Nbdf69e2c4eb040ea98fd31fa077936b5
4 schema:citation sg:pub.10.1023/a:1008344232130
5 schema:datePublished 2011-12
6 schema:datePublishedReg 2011-12-01
7 schema:description A map f : V: = GF(2m) → V is APN (almost perfect nonlinear) if its directional derivatives in nonzero directions are all 2-to-1. If m is greater than 2 and f vanishes at 0, then this derivative condition is equivalent to the condition that the binary linear code of length 2m − 1, whose parity check matrix has jth column equal to , is double-error-correcting, where ω is primitive in V. Carlet et al. (Designs Codes Cryptogr 15:125–156, 1998) proved that this code has dimension 2m − 1 − 2m; but their indirect proof uses a subtle argument involving general code parameter bounds to show that a double-error correcting code of this length could not be larger. We show here that this result follows immediately from a well-known result on bent functions ...a subject dear to the heart of Jacques Wolfmann.
8 schema:genre non_research_article
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf Nd041804fef1f441b98d5da6049aa4120
12 Nf5e46d5c60e44566b91852bd51fd65bb
13 sg:journal.1136695
14 schema:name On the dimension of an APN code
15 schema:pagination 275
16 schema:productId N176f64e5d11b44f8931d6c13a8373766
17 N77cfe756961445ea9c5e375de3f2f0c7
18 Nc7eb411d912b49f49fac66b0cd3fb5e4
19 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050580250
20 https://doi.org/10.1007/s12095-011-0049-z
21 schema:sdDatePublished 2019-04-10T21:39
22 schema:sdLicense https://scigraph.springernature.com/explorer/license/
23 schema:sdPublisher Ndbbd636b13dc44319361de81a30480cd
24 schema:url http://link.springer.com/10.1007%2Fs12095-011-0049-z
25 sgo:license sg:explorer/license/
26 sgo:sdDataset articles
27 rdf:type schema:ScholarlyArticle
28 N176f64e5d11b44f8931d6c13a8373766 schema:name readcube_id
29 schema:value f0f2640de8ad107652f11f031bc0f3aa952a9729218158f62a503603f8dec309
30 rdf:type schema:PropertyValue
31 N77cfe756961445ea9c5e375de3f2f0c7 schema:name dimensions_id
32 schema:value pub.1050580250
33 rdf:type schema:PropertyValue
34 Nbdf69e2c4eb040ea98fd31fa077936b5 rdf:first sg:person.016635145707.14
35 rdf:rest rdf:nil
36 Nc7eb411d912b49f49fac66b0cd3fb5e4 schema:name doi
37 schema:value 10.1007/s12095-011-0049-z
38 rdf:type schema:PropertyValue
39 Nd041804fef1f441b98d5da6049aa4120 schema:issueNumber 4
40 rdf:type schema:PublicationIssue
41 Ndbbd636b13dc44319361de81a30480cd schema:name Springer Nature - SN SciGraph project
42 rdf:type schema:Organization
43 Nf5e46d5c60e44566b91852bd51fd65bb schema:volumeNumber 3
44 rdf:type schema:PublicationVolume
45 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
46 schema:name Information and Computing Sciences
47 rdf:type schema:DefinedTerm
48 anzsrc-for:0804 schema:inDefinedTermSet anzsrc-for:
49 schema:name Data Format
50 rdf:type schema:DefinedTerm
51 sg:journal.1136695 schema:issn 1936-2447
52 1936-2455
53 schema:name Cryptography and Communications
54 rdf:type schema:Periodical
55 sg:person.016635145707.14 schema:affiliation https://www.grid.ac/institutes/grid.482831.4
56 schema:familyName Dillon
57 schema:givenName John F.
58 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016635145707.14
59 rdf:type schema:Person
60 sg:pub.10.1023/a:1008344232130 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027536103
61 https://doi.org/10.1023/a:1008344232130
62 rdf:type schema:CreativeWork
63 https://www.grid.ac/institutes/grid.482831.4 schema:alternateName National Security Agency
64 schema:name National Security Agency, 20755, Fort George G. Meade, MD, USA
65 rdf:type schema:Organization
 




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


...