1 Ocak 2021 Dergi makalesi Açık Erişim

Borello, Martino; Guneri, Cem; Sacikara, Elif; Sole, Patrick

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/236916</identifier>
  <creators>
    <creator>
      <creatorName>Borello, Martino</creatorName>
      <givenName>Martino</givenName>
      <familyName>Borello</familyName>
      <affiliation>Univ Paris 08, Univ Sorbonne Paris Nord, CNRS, UMR 7539,Lab Geometrie Analyse &amp; Applicat,LAGA, F-93430 Villetaneuse, France</affiliation>
    </creator>
    <creator>
      <creatorName>Guneri, Cem</creatorName>
      <givenName>Cem</givenName>
      <familyName>Guneri</familyName>
      <affiliation>Sabanci Univ, Fac Engn &amp; Nat Sci, TR-34956 Istanbul, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Sacikara, Elif</creatorName>
      <givenName>Elif</givenName>
      <familyName>Sacikara</familyName>
      <affiliation>Univ Zurich, Inst Math, Zurich, Switzerland</affiliation>
    </creator>
    <creator>
      <creatorName>Sole, Patrick</creatorName>
      <givenName>Patrick</givenName>
      <familyName>Sole</familyName>
      <affiliation>Aix Marseille Univ, CNRS, Ctr Marseille, I2M, Marseille, France</affiliation>
    </creator>
  </creators>
  <titles>
    <title>The Concatenated Structure Of Quasi-Abelian Codes</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2021</publicationYear>
  <dates>
    <date dateType="Issued">2021-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/236916</alternateIdentifier>
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  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1007/s10623-021-00921-4</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in Jitman and Ling (Des Codes Cryptogr 74:511-531, 2015), extending the analogous Chinese remainder decomposition of quasi-cyclic codes (Ling and Sole in IEEE Trans Inf Theory 47:2751-2760, 2001). We give a concatenated decomposition of quasi-abelian codes and show, as in the quasi-cyclic case, that the two decompositions are equivalent. The concatenated decomposition allows us to give a general minimum distance bound for quasi-abelian codes and to construct some optimal codes. Moreover, we show by examples that the minimum distance bound is sharp in some cases. In addition, examples of large strictly quasi-abelian codes of about a half rate are given. The concatenated structure also enables us to conclude that strictly quasi-abelian linear complementary dual codes over any finite field are asymptotically good.</description>
  </descriptions>
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