All Questions

Consider a vector $p =(p_1,\dots,p_n)$, $p_i>0$, $\sum p_i = 1$ and a matrix $M_{ij}$, which is doubly stochastic: $\sum_i M_{ij} = 1, \sum_j M_{ij} = 1, M_{ij} > 0$. Question 1 Just apply ...

In a paper on a proximity test for Reed-Solomon codes the authors state an "extremely optimistical" conjecture on the list decodability of Reed-Solomon codes (over prime fields $\mathbb F_q$)...

Update: In light of Fedor Petrov's answer, I added an additional requirement that all strings in $A$ and $B$ have Hamming weight exactly $n/2$, which hopefully makes the question more interesting. ...

Cross posted to theory exchange - https://cstheory.stackexchange.com/questions/45610/bounding-information-of-expression Suppose $u_1,\ldots,u_n$ are uniformly iid in $\{0,1\}$. Let $x_1,\ldots,x_n$ ...

Are there explicit or random construction of linear codes that achieve the $GV$ bound with polynomial time decodable property with alphabet size $q=2$? Tsfasman, Manin, Vladut beat the bound at ...