  The security of code-based cryptosystems such as the McEliece cryptosystem
relies primarily on the difficulty of decoding random linear codes. The best
decoding algorithms are all improvements of an old algorithm due to Prange:
they are known under the name of information set decoding techniques. It is
also important to assess the security of such cryptosystems against a quantum
computer. This research thread started in Overbeck and Sendrier's 2009 survey
on code-based cryptography, and the best algorithm to date has been Bernstein's
quantising of the simplest information set decoding algorithm, namely Prange's
algorithm. It consists in applying Grover's quantum search to obtain a
quadratic speed-up of Prange's algorithm. In this paper, we quantise other
information set decoding algorithms by using quantum walk techniques which were
devised for the subset-sum problem by Bernstein, Jeffery, Lange and Meurer.
This results in improving the worst-case complexity of $2^{0.06035n}$ of
Bernstein's algorithm to $2^{0.05869n}$ with the best algorithm presented here
(where $n$ is the codelength).
