Type II codes over F₂ + uF₂

The alphabet F₂ + uF₂ is viewed here as a quotient of the Gaussian integers by the ideal (2). Self-dual F₂ + uF₂ codes with Lee weights a multiple of 4 are called Type II. They give even uniniodular Gaussian lattices by Construction A, while Type I codes yield uniniodular Gaussian lattices. Construction B makes it possible to realize the Leech lattice as a Gaussian lattice. There is a Gray map which maps Type II codes into Type II binary codes with a fixed point free involution in their automorphism group. Combinatorial constructions use weighing matrices and strongly regular graphs. Gleason-type theorems for the symmetrized weight enumerators of Type II codes are derived. All self-dual codes are classified for length up to 8. The shadow of Type I codes yields bounds on the highest minimum Hamming and Lee weights.