-modular lattices from ternary codes
The alphabet where is viewed here as a quotient of the ring of integers of by the ideal (3). Self-dual codes for the hermitian scalar product give -modular lattices by construction . There is a Gray map which maps self-dual codes for the Euclidean scalar product into Type III codes with a fixed point free involution in their automorphism group. Gleason type theorems for the symmetrized weight enumerators of Euclidean self-dual codes and the length weight enumerator of hermitian self-dual...