3 problems

Let $G_{k\times 2k}$ be the $k\times 2k$ generator matrix whose columns are $e_1,e_2,\ldots,e_k,e_1+e_2,e_2+e_3,\ldots,e_{k-1}+e_k,e_k+e_1$, where $e_1,\ldots,e_k$ are the standard…

Let $C_0$ be an $(N,k)$-code that is MDS, and let $C$ be an $(n,k)$-code obtained by randomly puncturing $C_0$, meaning that its generator is formed by randomly selecting $n$ colum…

Let $R$ denote the coding rate, let $R_{\text{c2}}$ be the second critical rate, and let $\tau$ be the parameter in the lower-bound optimization for the typical random code (TRC) e…