• DocumentCode
    44936
  • Title

    Extremal Type I mathbb {Z}_{k} -Codes and k -Frames of Odd Unimodular Lattices

  • Author

    Harada, Masaaki

  • Author_Institution
    Res. Center for Pure & Appl. Math., Tohoku Univ., Sendai, Japan
  • Volume
    61
  • Issue
    1
  • fYear
    2015
  • fDate
    Jan. 2015
  • Firstpage
    72
  • Lastpage
    81
  • Abstract
    For some extremal (optimal) odd unimodular lattice L in dimensions 12, 16, 20, 28, 32, 36, 40, and 44, we determine all integers k such that L contains a k-frame. This result yields the existence of an extremal Type I Zk-code of lengths 12, 16, 20, 32, 36, 40, and 44, and a near-extremal Type I Zk-code of length 28 for positive integers k with only a few exceptions.
  • Keywords
    dual codes; extremal type I Zk-code; odd unimodular lattices k-frame; self-dual code; Educational institutions; Generators; Indexes; Lattices; Upper bound; Vectors; Zinc; Self-dual code; frame; unimodular lattice;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2014.2368563
  • Filename
    6960045
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=44936