Some Results on Type IV Codes Over

Dougherty, Gaborit, Harada, Munemasa, and Solé have previously given an upper bound on the minimum Lee weight of a Type IV self-dual -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 -code of length is at most 4 12 , except when = 4, and = 8 when the bound is 4, and = 16 when the bound is 8. We prove that the extremal binary doubly even self-dual codes of length 24 = 32 are not -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.