Lesson 2

Problem. Consider the degenerate case: \(d=n\). That is, we want the distance between any two codewords to be at least \(n\). What is the maximum size of the code in this case? More formally, compute the following: \[\max\{|C| \colon C \subseteq \{0,1\}^{n} \text{ and }\operatorname{dist}(s, t) \ge n \text{ for all \(s \neq t \in C\)}\}.\]