线性散列函数及其在检错和纠错中的应用
Linear hash-functions and their applications to error detection and correction
摘要：
我们描述和探索所谓的线性哈希函数，并展示如何使用它们来构建错误检测和纠正代码。该方法可以应用于不同类型的错误（例如，突发错误）。当该方法被应用到一个模型中的扭曲的字母的数量是有限的，其性能得到的估计是略好于已知的Varshamov-Gilbert界。我们还描述了随机码，其性能接近相同的边界，但它的构造要简单得多。在某些情况下，所得到的方法比已知的方法更简单，更灵活。特别地，所获得的错误检测码和公知的CRC码的复杂度接近，但是所提出的码与CRC不同，可以确定地检测其数量不超过预定限制的错误。
英文摘要：
We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is applied to a model where number of distorted letters is limited, the obtained estimate of its performance is slightly better than the known Varshamov-Gilbert bound. We also describe random code whose performance is close to the same boundary, but its construction is much simpler. In some cases the obtained methods are simpler and more flexible than the known ones. In particular, the complexity of the obtained error detection code and the well-known CRC code is close, but the proposed code, unlike CRC, can detect with certainty errors whose number does not exceed a predetermined limit.
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