4 problems

Hastings's conjecture. It is impossible to recover the quantum information with asymptotically vanishing error and probability greater than $1-t$.

A binary code is asymptotically optimal in the sense defined in Theorem 7 if its performance achieves the capacity of binary erasure channels (BECs) with the optimal scaling expone…

Transitive-code capacity conjecture. Under these assumptions, the sequence achieves capacity on the binary erasure channel under bit-MAP decoding. This conjecture proposes that tra…

Let $\{\mathcal{C}_n\}$ be a sequence of binary linear codes with blocklengths $N_n\to\infty$, rates $r_n\to r$ for some $r\in(0,1)$, and transitive permutation group for each code…