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iamp;#39;m glad to introduce our paper smoothing out binary linear codes and worst case sub-exponential hardness for airplane this is joint to work with john john that appears at crypto 2021 at the core of this work is worst case to average case reductions for erpn which is in turn based on smooth dilemma for binary linear codes this is the outline of this talk we will start with the preliminaries first of all binary linear codes linear means that we encode the message x by multiplying with a m by n matrix called the generator matrix binary means x over g of 2 namely every entry of the matrix of vector is either 0 or 1 and m as the length of the code word in general a good code has some non-trivial amount of minimum distance which is defined as the smallest hamming distance between all possible pairs of code words some previous work consider a strong strong version of hamming distance requirement called balanced code where this hamming distance has both the upper bound and the
