<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00151591</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-19T16:33:56+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="fr">Non linéarité des fonctions booléennes données par des traces de polynômes de degré binaire 3</title>
            <author role="aut">
              <persName>
                <forename type="first">François</forename>
                <surname>Rodier</surname>
              </persName>
              <email type="md5">3e3eec7df0468b5a17bb5a581d414c6c</email>
              <email type="domain">iml.univ-mrs.fr</email>
              <idno type="idhal" notation="numeric">828458</idno>
              <idno type="halauthorid" notation="string">56407-828458</idno>
              <affiliation ref="#struct-892"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Eric</forename>
                <surname>Férard</surname>
              </persName>
              <email type="md5">90b83156c9bb240a99f0126990ecf4d7</email>
              <email type="domain">upf.pf</email>
              <idno type="idhal" notation="numeric">839954</idno>
              <idno type="halauthorid" notation="string">205853-839954</idno>
              <affiliation ref="#struct-35430"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>François</forename>
                <surname>Rodier</surname>
              </persName>
              <email type="md5">3e3eec7df0468b5a17bb5a581d414c6c</email>
              <email type="domain">iml.univ-mrs.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2007-06-04 16:31:54</date>
              <date type="whenModified">2024-04-11 21:50:02</date>
              <date type="whenReleased">2007-06-04 16:37:40</date>
              <date type="whenProduced">2007-06-04</date>
              <date type="whenEndEmbargoed">2007-06-04</date>
              <ref type="file" target="https://hal.science/hal-00151591v1/document">
                <date notBefore="2007-06-04"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00151591v1/file/FerRod.pdf" id="file-151591-426289">
                <date notBefore="2007-06-04"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/0706.0447"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="100518">
                <persName>
                  <forename>François</forename>
                  <surname>Rodier</surname>
                </persName>
                <email type="md5">3e3eec7df0468b5a17bb5a581d414c6c</email>
                <email type="domain">iml.univ-mrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00151591</idno>
            <idno type="halUri">https://hal.science/hal-00151591</idno>
            <idno type="halBibtex">rodier:hal-00151591</idno>
            <idno type="halRefHtml">2007</idno>
            <idno type="halRef">2007</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-151591-426289"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="IML" corresp="I2M">Institut de Mathématiques de Luminy</idno>
            <idno type="stamp" n="I2M">Institut de Mathématiques de Marseille</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="UNIV-POLYNESIE">Université de la Polynésie française</idno>
            <idno type="stamp" n="UPF">Université de la Polynésie française </idno>
            <idno type="stamp" n="GAATI">GAATI - GEOMETRIE ALGEBRIQUE ET APPLICATIONS A LA THEORIE DE L'INFORMATION </idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="fr">Non linéarité des fonctions booléennes données par des traces de polynômes de degré binaire 3</title>
                <author role="aut">
                  <persName>
                    <forename type="first">François</forename>
                    <surname>Rodier</surname>
                  </persName>
                  <email type="md5">3e3eec7df0468b5a17bb5a581d414c6c</email>
                  <email type="domain">iml.univ-mrs.fr</email>
                  <idno type="idhal" notation="numeric">828458</idno>
                  <idno type="halauthorid" notation="string">56407-828458</idno>
                  <affiliation ref="#struct-892"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Eric</forename>
                    <surname>Férard</surname>
                  </persName>
                  <email type="md5">90b83156c9bb240a99f0126990ecf4d7</email>
                  <email type="domain">upf.pf</email>
                  <idno type="idhal" notation="numeric">839954</idno>
                  <idno type="halauthorid" notation="string">205853-839954</idno>
                  <affiliation ref="#struct-35430"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">0706.0447</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="fr">French</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Boolean function</term>
                <term xml:lang="en">nonlinearity</term>
                <term xml:lang="en">sum-of-square indicator</term>
                <term xml:lang="en">supersingular curves of genus 2</term>
              </keywords>
              <classCode scheme="classification">Primary 11T71; Secondary 06E30, 14H45</classCode>
              <classCode scheme="halDomain" n="math.math-nt">Mathematics [math]/Number Theory [math.NT]</classCode>
              <classCode scheme="halDomain" n="math.math-ag">Mathematics [math]/Algebraic Geometry [math.AG]</classCode>
              <classCode scheme="halDomain" n="info.info-cr">Computer Science [cs]/Cryptography and Security [cs.CR]</classCode>
              <classCode scheme="halDomain" n="info.info-dm">Computer Science [cs]/Discrete Mathematics [cs.DM]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We study the nonlinearity of functions defined on a finite field with 2^m elements which are the trace of a polynomial of degree 7 or more general polynomials of binary degree equal to 3. We show that for m odd such functions have rather good nonlinearity properties. We use for that recent results of Maisner and Nart about zeta functions of supersingular curves of genus 2.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-892" status="OLD">
          <idno type="RNSR">200412255H</idno>
          <orgName>Institut de mathématiques de Luminy</orgName>
          <orgName type="acronym">IML</orgName>
          <date type="start">1992-01-01</date>
          <date type="end">2011-01-01</date>
          <desc>
            <address>
              <addrLine>case 907 163 Av de Luminy 13288 MARSEILLE CEDEX 09</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://iml.univ-mrs.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR6206 / UPR9016" active="#struct-5033" type="direct"/>
            <relation name="UMR6206 / UPR9016" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-35430" status="VALID">
          <idno type="IdRef">277008867</idno>
          <idno type="RNSR">200415153H</idno>
          <orgName>Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information</orgName>
          <orgName type="acronym">GAATI</orgName>
          <desc>
            <address>
              <addrLine>Université de la Polynésie française 98702 Faa'a Tahiti</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://gaati.org/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300327" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-5033" status="OLD">
          <idno type="IdRef">026402882</idno>
          <orgName>Université de la Méditerranée - Aix-Marseille 2</orgName>
          <date type="start">1969</date>
          <date type="end">2011</date>
          <desc>
            <address>
              <addrLine>58, boulevard Charles Livon - 13284 Marseille cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univmed.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300327" status="VALID">
          <idno type="IdRef">067101925</idno>
          <idno type="ISNI">0000000121818619</idno>
          <idno type="ROR">https://ror.org/03ay59x86</idno>
          <orgName>Université de la Polynésie Française</orgName>
          <orgName type="acronym">UPF</orgName>
          <date type="start">1999-01-01</date>
          <desc>
            <address>
              <addrLine>BP6570 98702 FAAA - Polynésie française</addrLine>
              <country key="PF"/>
            </address>
            <ref type="url">https://www.upf.pf/fr</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>