Representation of antiuniform and partially antiuniform Huffman codes

A source S = {s₁,s₂, ..., s_n} having a binary Huffman code with code lengths satisfying l₁ = 1, l₂ = 2, ..., l_n = n - 1 is called an antiuniform source. If l₁ = 1, l₂ = 2, ..., l_i = i, then the source is called an i-level partially antiuniform source. In this paper we characterise these sources, and represent them by a system of linear inequalities. In addition, we determine the i-dimensional, 2 ≤ i ≤ n - 1, Euclidean projection of these two classes of sources.