<?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-00904783</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="2026-05-11T06:36:06+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Bounds on List Decoding of Rank-Metric Codes</title>
            <author role="aut">
              <persName>
                <forename type="first">Antonia</forename>
                <surname>Wachter-Zeh</surname>
              </persName>
              <email type="md5">a8b1a86001591d06d10b2f2969e63e3c</email>
              <email type="domain">univ-rennes1.fr</email>
              <idno type="idhal" notation="numeric">936542</idno>
              <idno type="halauthorid" notation="string">689216-936542</idno>
              <affiliation ref="#struct-75"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Marie-Annick</forename>
                <surname>Guillemer</surname>
              </persName>
              <email type="md5">6435e5e2a621104997686a9182756f34</email>
              <email type="domain">univ-rennes1.fr.invalid</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-11-15 11:09:21</date>
              <date type="whenModified">2025-04-01 12:52:05</date>
              <date type="whenReleased">2013-11-15 11:09:21</date>
              <date type="whenProduced">2013</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1301.4643"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="100376">
                <persName>
                  <forename>Marie-Annick</forename>
                  <surname>Guillemer</surname>
                </persName>
                <email type="md5">6435e5e2a621104997686a9182756f34</email>
                <email type="domain">univ-rennes1.fr.invalid</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00904783</idno>
            <idno type="halUri">https://hal.science/hal-00904783</idno>
            <idno type="halBibtex">wachterzeh:hal-00904783</idno>
            <idno type="halRefHtml">&lt;i&gt;IEEE Transactions on Information Theory&lt;/i&gt;, 2013, 59 (11), pp.7268-7277. &lt;a target="_blank" href="https://dx.doi.org/10.1109/TIT.2013.2274653"&gt;&amp;#x27E8;10.1109/TIT.2013.2274653&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">IEEE Transactions on Information Theory, 2013, 59 (11), pp.7268-7277. &amp;#x27E8;10.1109/TIT.2013.2274653&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-RENNES1">Université de Rennes 1</idno>
            <idno type="stamp" n="IRMAR">Institut de Recherche Mathématique de Rennes</idno>
            <idno type="stamp" n="UR2-HB">Université Rennes 2 - Haute Bretagne</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSA-RENNES">Institut National des Sciences Appliquées de Rennes</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="UNAM">l'unam - université nantes angers le mans</idno>
            <idno type="stamp" n="IRMAR-GAR">Géométrie algébrique réelle</idno>
            <idno type="stamp" n="UR1-HAL">Publications labos UR1 dans HAL-Rennes 1</idno>
            <idno type="stamp" n="UR1-MATH-STIC">UR1 - publications Maths-STIC</idno>
            <idno type="stamp" n="AGREENIUM">Archive ouverte en agrobiosciences</idno>
            <idno type="stamp" n="UNIV-RENNES2">Université Rennes 2</idno>
            <idno type="stamp" n="TEST-UNIV-RENNES">TEST Université de Rennes</idno>
            <idno type="stamp" n="TEST-UR-CSS">TEST Université de Rennes CSS</idno>
            <idno type="stamp" n="UNIV-RENNES">Université de Rennes</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="UR1-MATH-NUM">Pôle UnivRennes - Mathématiques - Numérique </idno>
            <idno type="stamp" n="INSTITUT-AGRO">Institut Agro</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Bounds on List Decoding of Rank-Metric Codes</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Antonia</forename>
                    <surname>Wachter-Zeh</surname>
                  </persName>
                  <email type="md5">a8b1a86001591d06d10b2f2969e63e3c</email>
                  <email type="domain">univ-rennes1.fr</email>
                  <idno type="idhal" notation="numeric">936542</idno>
                  <idno type="halauthorid" notation="string">689216-936542</idno>
                  <affiliation ref="#struct-75"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">5382</idno>
                <idno type="issn">0018-9448</idno>
                <title level="j">IEEE Transactions on Information Theory</title>
                <imprint>
                  <publisher>Institute of Electrical and Electronics Engineers</publisher>
                  <biblScope unit="volume">59</biblScope>
                  <biblScope unit="issue">11</biblScope>
                  <biblScope unit="pp">7268-7277</biblScope>
                  <date type="datePub">2013</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1301.4643</idno>
              <idno type="doi">10.1109/TIT.2013.2274653</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Constant-rank codes</term>
                <term xml:lang="en">Gabidulin codes</term>
                <term xml:lang="en">list decoding</term>
                <term xml:lang="fr">rank-metric codes</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-it">Computer Science [cs]/Information Theory [cs.IT]</classCode>
              <classCode scheme="halDomain" n="math.math-it">Mathematics [math]/Information Theory [math.IT]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>So far, there is no polynomial-time list decoding algorithm (beyond half the minimum distance) for Gabidulin codes. These codes can be seen as the rank-metric equivalent of Reed-Solomon codes. In this paper, we provide bounds on the list size of rank-metric codes in order to understand whether polynomial-time list decoding is possible or whether it works only with exponential time complexity. Three bounds on the list size are proven. The first one is a lower exponential bound for Gabidulin codes and shows that for these codes no polynomial-time list decoding beyond the Johnson radius exists. Second, an exponential upper bound is derived, which holds for any rank-metric code of length n and minimum rank distance d. The third bound proves that there exists a rank-metric code over F-qm of length n &lt;= m such that the list size is exponential in the length for any radius greater than half the minimum rank distance. This implies that there cannot exist a polynomial upper bound depending only on n and d similar to the Johnson bound in Hamming metric. All three rank-metric bounds reveal significant differences to bounds for codes in Hamming metric.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-75" status="OLD">
          <idno type="IdRef">028233107</idno>
          <idno type="RNSR">199612396W</idno>
          <idno type="ROR">https://ror.org/05y76vp22</idno>
          <orgName>Institut de Recherche Mathématique de Rennes</orgName>
          <orgName type="acronym">IRMAR</orgName>
          <date type="start">1996-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, bâtiments 22 et 23, 263 avenue du Général Leclerc, CS 7420535042  RENNES Cédex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://irmar.univ-rennes1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-105160" type="direct"/>
            <relation active="#struct-117606" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-247362" type="direct"/>
            <relation active="#struct-406201" type="direct"/>
            <relation name="UMR6625" active="#struct-441569" type="direct"/>
            <relation active="#struct-1090536" type="direct"/>
            <relation active="#struct-1042499" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-105160" status="VALID">
          <idno type="IdRef">26693823X</idno>
          <idno type="ROR">https://ror.org/015m7wh34</idno>
          <orgName>Université de Rennes</orgName>
          <orgName type="acronym">UR</orgName>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, 263 avenue Général Leclerc, CS 74205, 35042 RENNES CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-rennes.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-117606" status="VALID">
          <idno type="ROR">https://ror.org/04xaa4j22</idno>
          <orgName>Institut National des Sciences Appliquées - Rennes</orgName>
          <orgName type="acronym">INSA Rennes</orgName>
          <desc>
            <address>
              <addrLine>20, avenue des Buttes de Coësmes - CS 70839 - 35708 Rennes cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-rennes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-247362" status="VALID">
          <idno type="ROR">https://ror.org/03rxtdc22</idno>
          <orgName>École normale supérieure - Rennes</orgName>
          <orgName type="acronym">ENS Rennes</orgName>
          <desc>
            <address>
              <addrLine>Campus de Ker Lann - avenue Robert Schuman - 35170 Bruz</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-rennes.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-406201" status="VALID">
          <idno type="IdRef">054447658</idno>
          <idno type="ISNI">0000000121522279</idno>
          <idno type="ROR">https://ror.org/01m84wm78</idno>
          <orgName>Université de Rennes 2</orgName>
          <orgName type="acronym">UR2</orgName>
          <desc>
            <address>
              <addrLine>Place du recteur Henri Le Moal - CS 24307 - 35043 Rennes cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-rennes2.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-1090536" status="OLD">
          <idno type="ROR">https://ror.org/01s3fs709</idno>
          <orgName>INSTITUT AGRO Agrocampus Ouest</orgName>
          <date type="start">2020-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>65 rue de Saint Brieuc CS 84215 35042 Rennes CEDEX</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1042499" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-1042499" status="VALID">
          <idno type="IdRef">260373249</idno>
          <idno type="ROR">https://ror.org/01dkyve95</idno>
          <orgName>Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement</orgName>
          <orgName type="acronym">Institut Agro</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.institut-agro.fr</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>