1 Ocak 2021 Dergi makalesi Açık Erişim

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

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{
  "@context": "https://schema.org/", 
  "@id": 236916, 
  "@type": "ScholarlyArticle", 
  "creator": [
    {
      "@type": "Person", 
      "affiliation": "Univ Paris 08, Univ Sorbonne Paris Nord, CNRS, UMR 7539,Lab Geometrie Analyse & Applicat,LAGA, F-93430 Villetaneuse, France", 
      "name": "Borello, Martino"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey", 
      "name": "Guneri, Cem"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Univ Zurich, Inst Math, Zurich, Switzerland", 
      "name": "Sacikara, Elif"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Aix Marseille Univ, CNRS, Ctr Marseille, I2M, Marseille, France", 
      "name": "Sole, Patrick"
    }
  ], 
  "datePublished": "2021-01-01", 
  "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.", 
  "headline": "The concatenated structure of quasi-abelian codes", 
  "identifier": 236916, 
  "image": "https://aperta.ulakbim.gov.tr/static/img/logo/aperta_logo_with_icon.svg", 
  "license": "http://www.opendefinition.org/licenses/cc-by", 
  "name": "The concatenated structure of quasi-abelian codes", 
  "url": "https://aperta.ulakbim.gov.tr/record/236916"
}