  In a distributed storage system, private information retrieval (PIR)
guarantees that a user retrieves one file from the system without revealing any
information about the identity of its interested file to any individual server.
In this paper, we investigate $(N,K,M)$ coded sever model of PIR, where each of
$M$ files is distributed to the $N$ servers in the form of $(N,K)$ maximum
distance separable (MDS) code for some $N>K$ and $M>1$. As a result, we propose
a new capacity-achieving $(N,K,M)$ coded linear PIR scheme such that it can be
implemented with file length $\frac{K(N-K)}{\gcd(N,K)}$, which is much smaller
than the previous best result $K\big(\frac{N}{\gcd(N,K)}\big)^{M-1}$. Notably,
among all the capacity-achieving coded linear PIR schemes, we show that the
file length is optimal if $M>\big\lfloor
\frac{K}{\gcd(N,K)}-\frac{K}{N-K}\big\rfloor+1$, and within a multiplicative
gap $\frac{K}{\gcd(N,K)}$ of a lower bound on the minimum file length
otherwise.
