Some results on type IV codes over Z4

Dougherty, Gaborit, Harada, Munemasa and Sole (see ibid., vol.45, p.2345-60, 1999) have previously given an upper bound on the minimum Lee weight of a type IV self-dual Z₄-code, using a similar bound for the minimum distance of binary doubly even self-dual codes. We improve their bound, finding that the minimum Lee weight of a type IV self-dual Z₄-code of length n is at most 4[n/12], except when n=4, and n=8 when the bound is 4, and n=16 when the bound is 8. We prove that the extremal binary doubly even self-dual codes of length n⩾24, n≠32 are not Z₄-linear. We classify type IV-I codes of length 16. We prove that all type IV codes of length 24 have minimum Lee weight 4 and minimum Hamming weight 2, and the Euclidean-optimal type IV-I codes of this length have minimum Euclidean weight 8