Let C be a linear code of length n. We examine the following general problem: given a vector y, find the closest code vector to y. We focus on the algorithmic aspects of this problem. We discuss two groups of algorithms: gradient-like decoding and information set decoding. Together this covers most known general decoding methods.

This talk is partly based on joint works with A. Ashikhmin, and with E. Krouk and H.C.A. van Tilborg.

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