List Decodability at Small Radii

Yeow Meng Chee; Gennian Ge; Lijun Ji; San Ling; Jianxing Yin

List Decodability at Small Radii

Information Theory 2010-10-19 v1 Discrete Mathematics Combinatorics math.IT

Authors: Yeow Meng Chee , Gennian Ge , Lijun Ji , San Ling , Jianxing Yin

Abstract

$A'(n,d,e)$ , 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 $n$ .

Cite

@article{arxiv.1010.3312,
  title  = {List Decodability at Small Radii},
  author = {Yeow Meng Chee and Gennian Ge and Lijun Ji and San Ling and Jianxing Yin},
  journal= {arXiv preprint arXiv:1010.3312},
  year   = {2010}
}

Comments

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

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