Type II Codes over 4

The natural analogues of Lee weight and the Gray map over 4 are introduced. Self-dual codes for the Euclidean scalar product with Lee weights multiple of 4 are called Type II. They produce Type II binary codes by the Gray map. All extended Q-codes of length a multiple of 4 are Type II. This includes quadratic residue codes attached to a prime p≡3 (mod8), certain double circulant codes, and some affine invariant codes. A general mass formula is derived, a new upper bound for Euclidean self-dual codes over 4 is given, and the first extremal self-dual [92, 46, 16] binary code is built.