The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code generated by $\mathbf A$ has distance at most $k$. Here, $k$ ... more >>>

The k-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb{F}_2$, which can be stated as follows: given a generator matrix A and an integer k, determine whether the code generated by A has distance at most k, or in other words, whether ... more >>>

We show that assuming the strong exponential-time hypothesis (SETH), there are no non-trivial algorithms for the nearest codeword problem (NCP), the minimum distance problem (MDP), or the nearest codeword problem with preprocessing (NCPP) on linear codes over any finite field. More precisely, we show that there are no NCP, MDP, ... more >>>

We prove that the Minimum Distance Problem (MDP) on linear codes over any fixed finite field and parameterized by the input distance bound is W[1]-hard to approximate within any constant factor. We also prove analogous results for the parameterized Shortest Vector Problem (SVP) on integer lattices. Specifically, we prove that ... more >>>