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In his 2009 paper, Grover vs McElicee, Bernstein proposed to use the Grover's algorithm to obtain a quadratic speedup on the Prange ISD. However, it is not quite clear to me in which part of the algorithm a Grover search can be used and all other papers and references citing Bernstein's paper don't seem to clarify the point. Does anyone has any idea on this point?

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