The Main Theorems

  • Gabriele Nebe
  • Eric M. Rains
  • Neil J.A. Sloane
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 17)


This chapter will introduce the Clifford-Weil groups and their invariants. The main results of this book (Theorems 5.5.5 and 5.5.7) will be established in §5.5. They show that under quite general conditions, the invariant ring of the Clifford-Weil group C(ρ) associated with a finite representation ρ of a form ring is spanned by the complete weight enumerators of self-dual isotropic codes of Type ρ (and arbitrary length).


Form Ring Chain Ring Invariant Space Polynomial Invariant Isotropic Code 
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Copyright information

© Springer 2006

Authors and Affiliations

  • Gabriele Nebe
    • 1
  • Eric M. Rains
    • 2
  • Neil J.A. Sloane
    • 3
  1. 1.Lehrstuhl D für Mathematik Rheinisch-Westfälische Technische Hochschule AachenAachenGermany
  2. 2.Department of MathematicsUniversity of California at DavisDavisUSA
  3. 3.Internet and Network Systems Research AT&T Shannon LabsFlorham ParkUSA

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