To protect the information from disturbances created by noisy channels, redundant symbols (check symbols) with the information symbols are added. These extra symbols play important role for the efficiency of the communication system. It is always important to know how much these check symbols are required for a code designed for a specific purpose. In this communication, we give lower and upper bounds on check symbols needed to a linear code correcting key errors of length upto p which are confined to a single sub-block. We provide two examples of such linear codes. We, further, obtain those bounds for the case when key error occurs in the whole code length, but the number of disturbing components within key error is upto a certain number. Two examples in this case also are provided. KeywordsParity check matrix, Syndromes, Bounds, Key errors.

中文翻译：

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逐块和低密度密钥纠错码

为了保护信息免受噪声通道造成的干扰，添加了带有信息符号的冗余符号（校验符号）。这些额外的符号对于通信系统的效率起着重要的作用。知道为特定目的设计的代码需要多少校验符号总是很重要的。在这种通信中，我们给出了线性码所需的校验符号的上限和下限，该线性码可校正长度最大为p的关键错误，这些错误仅限于单个子块。我们提供了此类线性代码的两个示例。此外，我们获得了在整个代码长度中发生键错误，但键错误中的干扰分量数量达到一定数量的情况的边界。在这种情况下，还提供了两个示例。奇偶校验矩阵，综合症，界限，关键错误。