On the Minimum Weights of Type IV Codes over Z4 with Certain Lengths

Type IV self-dual codes over rings of order 4 have been introduced as self-dual codes over the rings with the property that all Hamming weights are even. The highest minimum Hamming, Lee and Euclidean weights of Type IV Z4-codes of lengths up to 40 and length 56 are known. In this paper, we prove that the optimal Type IV Z4-codes of lengths up to 72 have minimum Hamming, Lee and Euclidean weights at most 4, 8, and 16, respectively.