A recursive convolutional encoder can be regarded as an infinite impulse response system over the Galois Field of order 2. First, in this paper, we introduce finite response input sequences for recursive convolutional codes that give finite weight output sequences. In practice, we often need to describe the finite response sequence with a certain Hamming weight. Then, different properties of finite response input sequences are presented. It is shown that all finite response input sequences with a certain Hamming weight can be obtained in closed-form expressions from the so-called basic sequences. These basic sequences are presented for important recursive convolutional encoders and some possible applications are given .
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机译：递归卷积编码器可以通过Galois of Order第2条上的无限脉冲响应系统被视为无限脉冲响应系统2.首先，我们为递归卷积码引入有限响应输入序列，其提供有限权重输出序列。在实践中，我们经常需要描述具有一定的汉明重量的有限响应序列。然后，提出了有限响应输入序列的不同特性。结果表明，具有某种汉明重量的所有有限响应输入序列可以从所谓的基本序列的闭合表达中获得。对于重要的递归卷积编码器提供了这些基本序列，并给出了一些可能的应用。
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