1 Ocak 2021 Dergi makalesi Açık Erişim

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

Citation Style Language JSON

{
  "DOI": "10.1007/s10623-021-00921-4", 
  "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.", 
  "author": [
    {
      "family": "Borello", 
      "given": " Martino"
    }, 
    {
      "family": "Guneri", 
      "given": " Cem"
    }, 
    {
      "family": "Sacikara", 
      "given": " Elif"
    }, 
    {
      "family": "Sole", 
      "given": " Patrick"
    }
  ], 
  "container_title": "DESIGNS CODES AND CRYPTOGRAPHY", 
  "id": "236916", 
  "issued": {
    "date-parts": [
      [
        2021, 
        1, 
        1
      ]
    ]
  }, 
  "title": "The concatenated structure of quasi-abelian codes", 
  "type": "article-journal"
}