• DocumentCode
    61364
  • Title

    On Cyclic and Abelian Codes

  • Author

    Polcino Milies, Cesar ; Diniz de Melo, Fernanda

  • Author_Institution
    Inst. de Mat. e Estatistica, Univ. de Sao Paulo, São Paulo, Brazil
  • Volume
    59
  • Issue
    11
  • fYear
    2013
  • fDate
    Nov. 2013
  • Firstpage
    7314
  • Lastpage
    7319
  • Abstract
    In this paper, the minimum weight and the dimension of all cyclic codes of length pn over a field Fq, are computed, when p is an odd prime and Fq a finite field with q̅ elements, assuming that Fq generates the group of invertible elements of Zpn. Furthermore, the minimum weight and dimension of codes which are sum of two minimal codes in Fq(Cp×Cp) are also computed. Finally, the efficiency of cyclic codes and noncyclic abelian codes of length p2 are compared.
  • Keywords
    cyclic codes; cyclic codes; finite field; invertible elements; noncyclic Abelian codes; odd prime; Algebra; Equations; Hamming weight; Indexes; Lattices; Programming; Abelian code; convenience; cyclic code; group algebra; idempotent element; minimal code;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2013.2275111
  • Filename
    6570759
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=61364