Statistical Decoding of Codes over \(\mathbb{F}_q\)

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Abstract

In this paper we analyze statistical decoding over a finite field \(\mathbb{F}_q\) . We generalize Overbeck’s binary statistical decoding algorithm to codes over \(\mathbb{F}_q\) , and analyze the success probability of our algorithm. We provide experimental data for different field sizes. In addition to that, we describe two techniques how knowledge about structure of the code or of the solution can be used in order to speed up the decoding algorithm.