3 problems

Let $L$ be a positive integer, let $C\geq1$ be a positive real, and let $R=\frac{k}{n}$ be the rate of an $[n,k]$ Reed–Solomon code. A code is list-decodable from radius $\rho$ wit…

For a positive integer $n$, write $[n]=\{1,\ldots,n\}$. For subsets $I_1,\ldots,I_t\subseteq[n]$, define their weight by … and write…

For a code of rate $R$ over a finite field, list-decodable from relative radius $r$ with list size $L$ means that every Hamming ball of radius $r n$ contains at most $L$ codewords.…