A classification of Hadamard matrices of order $2p+2$ with an automorphism of order $p$ is given for $p=29$ and $31$. The ternary self-dual codes spanned by the newly found Hadamard matrices of order $60$ with an automorphism of order $29$ are computed, as well as the binary doubly even self-dual codes of length $120$ with generator matrices defined by related Hadamard designs. Several new ternary near-extremal self-dual codes, as well as binary near-extremal doubly even self-dual codes with previously unknown weight enumerators are found.

翻译：对于p=29和31的情况，给出了具有p阶自同构的2p+2阶Hadamard矩阵的分类。计算了由新发现的具有29阶自同构的60阶Hadamard矩阵生成的三元自对偶码，以及由相关Hadamard设计定义的生成矩阵所生成的120长二元双偶自对偶码。发现了若干新的三元近极值自对偶码，以及具有先前未知重量计数器的二元近极值双偶自对偶码。