We show that the ''majority is least stable'' conjecture is true for $n=1$ and $3$ and false for all odd $n\geq 5$.

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Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph. Combining good short codes together with a spectral expander graph yields the celebrated expander codes of Sipser ... more >>>

Multiplicity codes are a generalization of RS and RM codes where for each evaluation point we output the evaluation of a low-degree polynomial and all of its directional derivatives up to order $s$. Multi-variate multiplicity codes are locally decodable with the natural local decoding algorithm that reads values on a ... more >>>