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On the Fp-Linearity of the Generalized Gray Map Image of a \({Z_{{p^{k+1}}}}\)-Linear Code

  • H. Tapia-Recillas
  • G. Vega

Abstract

A necessary and sufficient condition for the generalized Gray map image G(D)of a \({Z_{{p^{k+1}}}}\)-linear code D to be F p -linear is given for any prime p and any integer k ≥1. If p = 2 and the linear code is assumed to be cyclic, a necessary condition for G(D)to be linear is also given in terms of the generators of the ideal of D. Some examples to illustrate the results are given.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • H. Tapia-Recillas
    • 1
  • G. Vega
    • 2
  1. 1.Dpto. MatemáticasUAM-IMéxico D.F.
  2. 2.Dirección General de Servicios de Cómputo Académico (DGSCA)UNAMMéxico D.F.México

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