Abstract
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 the 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. The proposed error correction codes are close to those obtained in the theory of linear codes, but there are examples when the proposed algorithms are more efficient.
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