List Decodability at Small Radii
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 $n$.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2010
- DOI:
- 10.48550/arXiv.1010.3312
- arXiv:
- arXiv:1010.3312
- Bibcode:
- 2010arXiv1010.3312M
- Keywords:
-
- Computer Science - Information Theory;
- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics
- E-Print:
- to appear in Designs, Codes, and Cryptography (accepted October 2010)