• DocumentCode
    1197594
  • Title

    On the structure of linear codes with covering radius two and three

  • Author

    Struik, Rene

  • Author_Institution
    Dept. of Math. & Comput. Sci., Eindhoven Univ. of Technol., Netherlands
  • Volume
    40
  • Issue
    5
  • fYear
    1994
  • fDate
    9/1/1994 12:00:00 AM
  • Firstpage
    1406
  • Lastpage
    1416
  • Abstract
    We obtain new bounds on l(m,r), the minimum length of a linear code with codimension m and covering radius r. All bounds are derived in a uniform way. We employ results from coding theory, some earlier results on covering codes, and combinatorial arguments. We prove the following bounds: l(6, 2)=13, l(7,2)=19, l(8,2)⩾25, l(9,2)⩾34, l(2m-l,2)⩾2m+1 for m⩾3, l(14,2)⩾182, l(16,2)⩾363, l(18,2)⩾725, l(20,2)⩾1449, l(22,2)⩾2897, l(24,2)⩾5794, l(9,3)⩾17, l(10,3)⩾21, l(12,3)⩾31, l(13,3)⩾38
  • Keywords
    block codes; encoding; binary block codes; bounds; codimension; coding theory; covering codes; covering radius; linear codes; minimum code length; Block codes; Error correction codes; Hamming distance; Information theory; Linear code; Mathematics; Meetings;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.333857
  • Filename
    333857
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1197594