Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full propelinear codes turns out. We prove that their existence is equivalent to the existence of central relative (v, w, v, v/w)-difference sets. Moreover, some structural properties of these codes are studied and examples are provided. Some of the propelinear codes constructed for the examples perform better than any comparable linear code.

中文翻译：

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广义Hadamard全正则码

来自广义Hadamard矩阵的代码已经引入。当广义Hadamard矩阵是共循环的时，我们在这里处理这些代码。结果，出现了一种新的代码类型，我们称之为广义Hadamard完全线性代码。我们证明它们的存在等于中心相对（v，  w，  v，  v / w）差集的存在。此外，研究了这些代码的一些结构特性并提供了示例。为示例构造的某些直线代码的性能优于任何可比较的线性代码。