Question 62
Let $n, k$ be positive integers such that $n \ge k$. Find the maximum number of binary sequences of length $n$ such that by fixing any arbitrary $k$ bits, the achieved sequences do not produce all binary sequences of length $k$. For example if $k = 1$, we can only have one sequence, otherwise they will differ in at least one bit which means that fixing that bit produces all binary sequences of length 1.