Two Corollaries to the Huffman Coding Procedure

For a given set of
N
symbols to be coded by a code of alphabet size
D
, the necessary and sufficient conditions for the optimality of a block code of length
m
, if
N = D^m
, and the optimality of a code of words of length only
m
and
m + 1
, if
D^m < N < D^{m+1}
, are stated, and an example of the construction of such a code is given.