Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Capacity-Achieving $T$-PIR Scheme Based On MDS Array Codes   Suppose a database containing $M$ records is replicated in each of $N$
servers, and a user wants to privately retrieve one record by accessing the
servers such that identity of the retrieved record is secret against any up to
$T$ servers. A scheme designed for this purpose is called a $T$-private
information retrieval ($T$-PIR) scheme.
  In this paper we focus on the field size of $T$-PIR schemes. We design a
generalcapacity-achieving $T$-PIR scheme whose queries are generated by using
some {\rm MDS } array codes. It only requires field size $q\geq\sqrt[\ell]{N}$,
where $\ell=\min\{t^{M-2},(n-t)^{M-2}\}$, $~t=T/{\rm gcd}(N,T)$,$~n=N/{\rm
gcd}(N,T)$ and has the optimal sub-packetization $Nn^{M-2}$. Comparing with
existing capacity-achieving $T$-PIR schemes, our scheme has the following
advantage, that is, its field size monotonically decreases as the number of
records $M$ grows. In particular, the binary field is sufficient for building a
capacity-achieving T-PIR scheme as long as $M\geq
2+\lceil\log_\mu\log_2N\rceil$, where $\mu=\min\{t,n-t\}>1$.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th