• DocumentCode
    745834
  • Title

    The rank and kernel of extended 1-perfect Z4-linear and additive non-Z4-linear codes

  • Author

    Borges, Joaquim ; Phelps, Kevin T. ; Rifà, Josep

  • Author_Institution
    Comput. Sci. Dept., Univ. Autonoma de Barcelona, Bellaterra, Spain
  • Volume
    49
  • Issue
    8
  • fYear
    2003
  • Firstpage
    2028
  • Lastpage
    2034
  • Abstract
    A binary extended 1-perfect code of length n + 1 = 2t is additive if it is a subgroup of Z2α × Z4β. The punctured code by deleting a Z2 coordinate (if there is one) gives a perfect additive code. 1-perfect additive codes were completely characterized and by using that characterization we compute the possible parameters α, β, rank, and dimension of the kernel for extended 1-perfect additive codes. A very special case is that of extended 1-perfect Z4-linear codes.
  • Keywords
    binary codes; linear codes; 1-perfect additive codes; additive non-4-linear codes; binary extended 1-perfect code; dimension; extended 1-perfect 4-linear code; kernel; punctured code; rank; subgroup; Additives; Arithmetic; Binary codes; Combinatorial mathematics; Computer science; Hamming distance; Kernel; Linear code; Propulsion;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2003.814490
  • Filename
    1214081
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=745834