Optimum Extendible Prefix Codes

Suppose that we have L messages coded by a prefix code (over an alphab et 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 rea sons), 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 effcient algorithm to construct the opti mum extension of a non-complete prefix code, provided the initial code is optimal. 1.) Proceedings of the First Japan-New Zealand Workshop on Logic in Computer Science, special issue editors D.S. Bridges, C.S. Calude, M.J. Dinneen and B. Khoussainov.