Approximate Local Decoding of Cubic Reed-Muller Codes Beyond the List Decoding Radius

SODA '18: Symposium on Discrete Algorithms New Orleans Louisiana January, 2018, pp. 663-679, 2018.

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Abstract:

We consider the question of decoding Reed-Muller codes over Fn2 beyond their list-decoding radius. Since, by definition, in this regime one cannot demand an efficient exact list-decoder, we seek an approximate decoder: Given a word F and radii r' > r > 0, the goal is to output a codeword within radius r' of F, if there exists a codeword w...More

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