We give a new definition of generalized Hamming weights of nonlinear codes and a new interpretation connected with it. These generalized weights are determined by the entropy/length profile of the code. We show that this definition characterizes the performance of nonlinear codes on the wire-tap channel of type II. The new definition is invariant under translates of the code, it satisfies the property of strict monotonicity and the generalized Singleton bound. We check the relations between the generalized weight hierarchies of Z/sub 4/-linear codes and their binary image under the Gray map. We also show that the binary image of a Z/sub 4/-linear code is a symmetric, not necessarily rectangular code. Moreover, if this binary image is a linear code then it admits a twisted squaring construction.
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机译：我们给出了非线性代码的广义汉明权重的新定义以及与此相关的新解释。这些广义权重由代码的熵/长度分布确定。我们表明，该定义表征了类型II的窃听通道上的非线性代码的性能。新的定义在代码翻译后是不变的，它满足严格单调性和广义Singleton界的性质。我们检查了Z / sub 4 /线性码的广义权重层次结构与其在Gray映射下的二进制图像之间的关系。我们还显示Z / sub 4 /线性代码的二进制图像是对称的，不一定是矩形代码。此外，如果此二进制图像是线性代码，则它允许使用扭曲的平方结构。
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