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We describe and explore so-called linear hash functions and show how they canbe used to build error detection and correction codes. The method can beapplied for different types of errors (for example, burst errors). When themethod is applied to a model where number of distorted letters is limited, theobtained estimate of its performance is slightly better than the knownVarshamov-Gilbert bound. We also describe random code whose performance isclose to the same boundary, but its construction is much simpler. In some casesthe obtained methods are simpler and more flexible than the known ones. Inparticular, the complexity of the obtained error detection code and thewell-known CRC code is close, but the proposed code, unlike CRC, can detectwith certainty errors whose number does not exceed a predetermined limit.

Linear hash-functions and their applications to error detection and correction