List Decodability at Small Radii

Details List Decodability at Small Radii List Decodability at Small Radii

2010-10-16

arxiv.org/abs/1010.3312v1

Computer Science

Information Theory

to appear in Designs, Codes, and Cryptography (accepted October 2010)

Scientific paper

$A'(n,d,e)$, the smallest $\ell$ for which every binary error-correcting code
of length $n$ and minimum distance $d$ is decodable with a list of size $\ell$
up to radius $e$, is determined for all $d\geq 2e-3$. As a result, $A'(n,d,e)$
is determined for all $e\leq 4$, except for 42 values of $n$.

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