Optimal binary one-ended codes

Binary prefix-free codes in which all codewords end with a "1" have been introduced by Berger and Yeung (1990). A recursive method is given here for the construction of all optimal "1"-ended codes with n codewords. It is shown that the set of codes obtained by the construction contains only optimal codes. We also compute recursively the number of essentially different optimal "1"-ended codes with n codewords and show that their number grows faster than any polynomial in n.