We show that from every skew-type Hadamard matrix of order 4t one can obtain a series of skew-type Hadamard matrices of order \(2^{i+2}t\), i a positive integer, whose binary linear codes are doubly even self-dual binary codes of length \(2^{i+2}t\). It is known that a doubly even self-dual binary code yields an even unimodular lattice. Hence, this construction of skew-type Hadamard matrices gives us a series of even unimodular lattices of rank \(2^{i+2}t\), i a positive integer. Furthermore, we provide a construction of doubly even self-dual binary codes from conference graphs.

中文翻译：

---

从 Hadamard 矩阵构造双偶自对偶码甚至幺模格

我们证明，从每个 4 t阶的斜型 Hadamard 矩阵中，可以得到一系列阶为\(2^{i+2}t\)的斜型 Hadamard 矩阵，i为正整数，其二进制线性码为长度为\(2^{i+2}t\)的双偶自对偶二进制码。已知双偶自对偶二进制码产生偶单模格。因此，这种斜型 Hadamard 矩阵的构造为我们提供了一系列秩为\(2^{i+2}t\)的偶单模格子，i是一个正整数。此外，我们还从会议图中提供了双偶自对偶二进制代码的构造。