List decodability at small radii

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چکیده

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List decodability at small radii

A′(n,d,e), the smallest ` for which every binary error-correcting code of length n and minimum distance d is decodable with a list of size ` up to radius e, is determined for all d ≥ 2e−3. As a result, A′(n,d,e) is determined for all e≤ 4, except for 42 values of n.

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List Decodability of Random Linear Concatenated Codes

“ј . These results are shown by choosing the code at random. However, as we saw in Chapter 4 the explicit constructions of codes over finite alphabets are nowhere close to achieving list-decoding capacity. The linear codes in Chapter 4 are based on code concatenation. A natural question to ask is whether linear codes based on code concatenation can get us to list-decoding capacity for fixed al...

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On the List-Decodability of Random Linear Rank-Metric Codes

The list-decodability of random linear rank-metric codes is shown to match that of random rank-metric codes. Specifically, an Fq-linear rank-metric code over F m×n q of rate R = (1 − ρ)(1 − n m ρ) − ε is shown to be (with high probability) list-decodable up to fractional radius ρ ∈ (0, 1) with lists of size at most Cρ,q ε , where Cρ,q is a constant depending only on ρ and q. This matches the bo...

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On the List Decodability of Self-orthogonal Rank Metric Codes

V. Guruswami and N. Resch prove that the list decodability of Fq-linear rank metric codes is as good as that of random rank metric codes in [17]. Due to the potential applications of self-orthogonal rank metric codes, we focus on list decoding of them. In this paper, we prove that with high probability, an Fq-linear self-orthogonal rank metric code over Fn×m q of rate R = (1 − τ)(1 − n mτ) − is...

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Forming parts over small radii

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ژورنال

عنوان ژورنال: Designs, Codes and Cryptography

سال: 2010

ISSN: 0925-1022,1573-7586

DOI: 10.1007/s10623-010-9445-1