论文标题
线性哈希函数及其在错误检测和校正中的应用
Linear hash-functions and their applications to error detection and correction
论文作者
论文摘要
我们描述和探索所谓的线性哈希功能，并展示如何用于构建错误检测和校正代码。该方法可以应用于不同类型的错误（例如，爆发错误）。当该方法应用于损坏字母数量受到限制的模型时，获得的性能的估计值略优于已知的Varshamov-Gilbert结合。我们还描述了其性能接近相同边界的随机代码，但其构造要简单得多。在某些情况下，获得的方法比已知的方法更简单，更灵活。特别是，获得的错误检测代码和众所周知的CRC代码的复杂性是接近的，但是与CRC不同的代码可以用确定性错误检测，其数字不超过预定的限制。
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.
