The symmetry group of ℤqn in the Lee space and the ℤqn-linear codes

  • Sueli Rodrigues Costa
  • João Roberto Gerônimo
  • Reginaldo PalazzoJr.
  • J. Carmelo Interlando
  • Marcelo Muniz Silva Alves
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1255)


The ℤ4-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the ℤ4-linearity to ℤ q n -linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (ℤ q n , d L ), as one of the most interesting spaces for coding applications.We establish the symmetry group of ℤ q n for any n and q by determining its isometries.We also show that there is no cyclic subgroup of order q n in Γ(ℤ q n ) acting transitively in ℤ q n . Therefore, there exists no ℤ q n -linear code with respect to the cyclic subgroup.


Symmetry Group Linear Code Cyclic Subgroup Dihedral Group Zero Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Sueli Rodrigues Costa
    • 1
  • João Roberto Gerônimo
    • 2
  • Reginaldo PalazzoJr.
    • 3
  • J. Carmelo Interlando
    • 4
  • Marcelo Muniz Silva Alves
    • 5
  1. 1.Institute of Mathematics and StatisticsIMECC-UNICAMPBrazil
  2. 2.Department of Mathematics, Institute of Exact SciencesMaringa State University, UEMBrazil
  3. 3.Department of Telematics, Faculty of Electrical and Computer EngineeringUNICAMPBrazil
  4. 4.Department of MathematicsPaulista State University, UNESPBrazil
  5. 5.Ph.D. Program. Institute of Mathematics and StatisticsIMECC-UNICAMPBrazil

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