For every constant gamma >= 1, k-Even Set is W[1]-hard to approximate under randomized reductions, and for every p > 1, k-SVP in the l_p norm is W[1]-hard to approximate to some constant factor.
A simple deterministic reduction for the gap minimum distance of code problem
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Parameterized Intractability of Even Set and Shortest Vector Problem
For every constant gamma >= 1, k-Even Set is W[1]-hard to approximate under randomized reductions, and for every p > 1, k-SVP in the l_p norm is W[1]-hard to approximate to some constant factor.