Finite Completion of Comma-Free Codes. Part I

Abstract

In this paper we consider (finite) comma-free codes and their completion problem. We sketch a few lines on their origin, history and development. Comma-free codes were defined rigorously in 1958, as mathematical objects, in Golomb, Gordon and Welch [], although a rudimentary notion had been suggested by Crick, Griffith and Orgel earlier in 1957 [], in connection with the famous discovery of DNA structure; for more details on the biological origin of the problem, see [], or [], annotation to Chap. VII.During the late 1950s and the 1960s there had been quite extensive investigation on comma-free codes of constant length (block codes), free from biological considerations. Then the main line of study was concerned with the maximal size of comma-free codes of a given length and on alphabets with a fixed number of letters. The most impressive achievement was a proof by Eastman [] of a conjecture of Golomb, Gordon and Welch [] on the maximal number of words in a comma-free code on k-letter alphabet, k odd; see [], Chap. VII] for alternative proofs.