  The problem of symmetric private information retrieval (SPIR) from a coded
database which is distributively stored among colluding servers is studied.
Specifically, the database comprises $K$ files, which are stored among $N$
servers using an $(N,M)$-MDS storage code. A user wants to retrieve one file
from the database by communicating with the $N$ servers, without revealing the
identity of the desired file to any server. Furthermore, the user shall learn
nothing about the other $K-1$ files in the database. In the $T$-colluding SPIR
problem (hence called TSPIR), any $T$ out of $N$ servers may collude, that is,
they may communicate their interactions with the user to guess the identity of
the requested file. We show that for linear schemes, the information-theoretic
capacity of the MDS-TSPIR problem, defined as the maximum number of information
bits of the desired file retrieved per downloaded bit, equals
$1-\frac{M+T-1}{N}$, if the servers share common randomness (unavailable at the
user) with amount at least $\frac{M+T-1}{N-M-T+1}$ times the file size.
Otherwise, the capacity equals zero. We conjecture that our capacity holds also
for general MDS-TSPIR schemes.
