1 Ocak 2021 Dergi makalesi Açık Erişim

Baran, Esma; Sahin, Mesut

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/232398</identifier>
  <creators>
    <creator>
      <creatorName>Baran, Esma</creatorName>
      <givenName>Esma</givenName>
      <familyName>Baran</familyName>
    </creator>
    <creator>
      <creatorName>Sahin, Mesut</creatorName>
      <givenName>Mesut</givenName>
      <familyName>Sahin</familyName>
      <affiliation>Hacettepe Univ, Dept Math, Ankara, Turkey</affiliation>
    </creator>
  </creators>
  <titles>
    <title>On Parameterized Toric 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/232398</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1007/s00200-021-00513-8</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">LeT(X) be a complete simplicial toric variety over a finite field with a split torus T-X. For any matrix Q, we are interested in the subgroup Y-Q of T-X parameterized by the columns of Q. We give an algorithm for obtaining a basis for the unique lattice L whose lattice ideal I-L is I(Y-Q). We also give two direct algorithmic methods to compute the order of Y-Q, which is the length of the corresponding code C-alpha,C-YQ. We share procedures implementing them in Macaulay2. Finally, we give a lower bound for the minimum distance of C-alpha,C-YQ, taking advantage of the parametric description of the subgroup Y-Q. As an application, we compute the main parameters of the toric codes on Hirzebruch surfaces H-l generalizing the corresponding result given by Hansen.</description>
  </descriptions>
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