Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > ERROR CORRECTION:
Reports tagged with error correction:
TR02-059 | 9th August 2002
Iordanis Kerenidis, Ronald de Wolf

#### Exponential Lower Bound for 2-Query Locally Decodable Codes

We prove exponential lower bounds on the length of 2-query
locally decodable codes. Goldreich et al. recently proved such bounds
for the special case of linear locally decodable codes.
Our proof shows that a 2-query locally decodable code can be decoded
with only 1 quantum query, and then ... more >>>

TR15-116 | 21st July 2015
Joshua Brakensiek, Venkatesan Guruswami, Samuel Zbarsky

#### Efficient Low-Redundancy Codes for Correcting Multiple Deletions

Revisions: 1

We consider the problem of constructing binary codes to recover from $k$-bit deletions with efficient encoding/decoding, for a fixed $k$. The single deletion case is well understood, with the Varshamov-Tenengolts-Levenshtein code from 1965 giving an asymptotically optimal construction with $\approx 2^n/n$ codewords of length $n$, i.e., at most $\log n$ ... more >>>

TR15-117 | 21st July 2015
Boris Bukh, Venkatesan Guruswami

#### An improved bound on the fraction of correctable deletions

Revisions: 1

We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion fraction approaching $1-\frac{2}{k+1}$. In particular, for binary codes, we are able to ... more >>>

ISSN 1433-8092 | Imprint