1 Ocak 2021 Dergi makalesi Açık Erişim

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

Dublin Core

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  <dc:creator>Borello, Martino</dc:creator>
  <dc:creator>Guneri, Cem</dc:creator>
  <dc:creator>Sacikara, Elif</dc:creator>
  <dc:creator>Sole, Patrick</dc:creator>
  <dc:date>2021-01-01</dc:date>
  <dc:description>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.</dc:description>
  <dc:identifier>https://aperta.ulakbim.gov.trrecord/236916</dc:identifier>
  <dc:identifier>oai:aperta.ulakbim.gov.tr:236916</dc:identifier>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:source>DESIGNS CODES AND CRYPTOGRAPHY</dc:source>
  <dc:title>The concatenated structure of quasi-abelian codes</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
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