  The NP-hard problem of decoding random linear codes is crucial to both coding
theory and cryptography. In particular, this problem underpins the security of
many code based post-quantum cryptographic schemes. The state-of-art algorithms
for solving this problem are the information syndrome decoding algorithm and
its advanced variants. In this work, we consider syndrome decoding in the
multiple instances setting. Two strategies are applied for different scenarios.
The first strategy is to solve all instances with the aid of the precomputation
technique. We adjust the current framework and distinguish the offline phase
and online phase to reduce the amortized complexity. Further, we discuss the
impact on the concrete security of some post-quantum schemes. The second
strategy is to solve one out of many instances. Adapting the analysis for some
earlier algorithm, we discuss the effectiveness of using advanced variants and
confirm a related folklore conjecture.
