  Minimum storage regenerating (MSR) codes, with the MDS property and the
optimal repair bandwidth, are widely used in distributed storage systems (DSS)
for data recovery. In this paper, we consider the construction of $(n,k,l)$ MSR
codes in the centralized model that can repair $h$ failed nodes simultaneously
with $e$ out $d$ helper nodes providing erroneous information. We first propose
the new repair scheme, and give a complete proof of the lower bound on the
amount of symbols downloaded from the helped nodes, provided that some of
helper nodes provide erroneous information. Then we focus on two explicit
constructions with the repair scheme proposed. For $2\leq h\leq n-k$, $k+2e\leq
d \leq n-h$ and $d\equiv k+2e \;(\mod{h})$, the first one has the UER $(h,
d)$-optimal repair property, and the second one has the UER $(h, d)$-optimal
access property. Compared with the original constructions (Ye and Barg, IEEE
Tran. Inf. Theory, Vol. 63, April 2017), our constructions have improvements in
three aspects: 1) The proposed repair scheme is more feasible than the
one-by-one scheme presented by Ye and Barg in a parallel data system; 2) The
sub-packetization is reduced from $\left(\operatorname{lcm}(d-k+1,
d-k+2,\cdots, d-k+h)\right)^n$ to $\left((d-2e-k+h)/h\right)^n$, which reduces
at least by a factor of $(h(d-k+h))^n$; 3) The field size of the first
construction is reduced to $|\mathbb{F}| \geq n(d-2e-k+h)/h$, which reduces at
least by a factor of $h(d-k+h)$. Small sub-packetization and small field size
are preferred in practice due to the limited storage capacity and low
computation complexity in the process of encoding, decoding and repairing.
