Optimum Extendible Prefix Codes

Suppose that we have L messages coded by a prefix code (over an alphabet M with m letters) having a minimum weighted length. The problem addressed in this paper is the following: How to find s codewords for new messages so that by leaving unchanged the codification of the first L messages (by compatibility reasons), the resulting extended code is still prefix (over M) and has a minimum weighted length? To this aim we introduce the notion of optimum extendible prefix code and then, by modifying Huffman’s algorithm, we give an efficient algorithm to construct the optimum extension of a non-complete prefix code, provided the initial code is optimal.