Another way to view a binary prefix code is as the set of leaves on a unique binary tree. Each leaf corresponds to a codeword, given by the path of dots and dashes from the root. We can start with a binary tree consisting only of such a path to (C_1). To find an answer, we can continue adding nodes (without touching (C_1)'s leaf) until we have enough.
Implementation-wise, we can imagine a perfect binary tree that's pruned at the leaf corresponding to (C_1). Breadth-first search can be used to perform a level-order traversal of this tree without explicitly constructing it. Each node can be represented as a candidate codeword string, with children obtained by appending either a dot or dash.
As we BFS, we maintain all the current leaves (nodes enqueued but have yet to be processed), stopping once we hit (N - 1) leaves. We must be careful not to output anything on the path to (C_1). This can be handled by avoiding outputting prefixes of (C_1) or (C_1)-prefixed codewords, or by simply by prepending all output codewords with the opposite of (C_1)'s first character (essentially pruning the perfect binary tree at the start of (C_1) instead of the end).
Since a perfect binary tree of height (h) has (2^h) leaves, a maximum codeword length (tree height) of (10) still yields (2^{10} = 1024) leaves to work with. Since pruning once cannot get rid of more than (1/2) of a tree's leaves, we'll get at least (1024/2 = 512 > 100) leaves before hitting length (10).
Another approach, yielding a slightly longer total output length, is to generate bitstrings of a fixed length ((\lceil \log_2 N \rceil + 1) is sufficient), excluding any which prefixes or is prefixed by (C_1).