In this work we adapt the notion of non-malleability for codes or Dziembowski, Pietrzak and Wichs (ICS 2010) to locally testable codes. Roughly speaking, a locally testable code is non-malleable if any tampered codeword which passes the local test with good probability is close to a valid codeword which either ... more >>>

The $d$-to-$1$ conjecture of Khot asserts that it is hard to satisfy an $\epsilon$ fraction of constraints of a satisfiable $d$-to-$1$ Label Cover instance, for arbitrarily small $\epsilon > 0$. We prove that the $d$-to-$1$ conjecture for any fixed $d$ implies the hardness of coloring a $4$-colorable graph with $C$ ... 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 >>>