CiteULike is a free online bibliography manager. Register and you can start organising your references online.
Tags

# Query-Efficient Locally Decodable Codes of Subexponential Length

Computational Complexity (10 Aug 2011), pp. 1-31, doi:10.1007/s00037-011-0017-1  Key: citeulike:11546064

## Likes (beta)

This copy of the article hasn't been liked by anyone yet.

### Abstract

We develop the algebraic theory behind the constructions of Yekhanin (2008) and Efremenko (2009), in an attempt to understand the “algebraic niceness” phenomenon in $\mathbbZ_m$. We show that every integer $m = pq = 2^t -1$, where $p$, $q$ and $t$ are prime, possesses the same good algebraic property as $m=511$ that allows savings in query complexity. We identify 50 numbers of this form by computer search, which together with 511, are then applied to gain improvements on query complexity via Itoh and Suzuki's composition method. More precisely, we construct a $3^\lceil r/2\rceil$-query LDC for every positive integer $r<104$ and a $≤ft\lfloor (3/4)^51⋅ 2^r\right\rfloor$-query LDC for every integer $r≥ 104$, both of length $N_r$, improving the $2^r$ queries used by Efremenko (2009) and $3⋅ 2^r-2$ queries used by Itoh and Suzuki (2010). We also obtain new efficient private information retrieval (PIR) schemes from the new query-efficient LDCs.