Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 06, 2021, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Saeed Ilchi

On List Decoding of Reed-Solomon Codes

A code over alphabet Σ and with block length n is (ρ,L)-list decodable if any hamming ball of radius ρn in Σⁿ contains at most L codewords. We are interested in maximum ρ where the code is (ρ,L=poly(n))-list decodable.

For Reed-Solomon codes with arbitrary evaluation points, we cannot expect a rate significantly better than ε² to list decode up to radius 1-ε. This indeed matches the Johnson bound. Although, it has shown that if we take an RS-code with random evaluation points, the rate becomes Õ(ε). Moreover, the list size is constant, say O(1/ε). We will discuss this result based on the works of Shangguan, and Tamo (https://arxiv.org/abs/1911.01502), and Guo, Li, Shangguan, Tamo, and Wootters (https://arxiv.org/abs/2011.04453).

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