Applications of Coding Theory to the Construction of Modular Lattices

@article{Bachoc1997ApplicationsOC,
  title={Applications of Coding Theory to the Construction of Modular Lattices},
  author={Christine Bachoc},
  journal={J. Comb. Theory, Ser. A},
  year={1997},
  volume={78},
  pages={92-119}
}
  • C. Bachoc
  • Published 1 April 1997
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
We study self-dual codes over certain finite rings which are quotients of quadratic imaginary fields or of totally definite quaternion fields over Q. A natural weight taking two different nonzero values is defined over these rings; using invariant theory, we give a basis for the space of invariants to which belongs the three variables weight enumerator of a self-dual code. A general bound for the weight of such codes is derived. We construct a number of extremal self-dual codes, which are the… 
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