Traceability codes are identifiable parent property (IPP) codes with the additional requirement that the Hamming distance can be used to trace a parent of a word. Traceability codes can be used for constructing digital fingerprints in order to deter users from illegally copying digital data. We construct a class of traceability codes and determine the exact parameters of some of the codes in this class.

The problem of determining the maximum size of a ternary code is considered, under the restriction that each symbol should appear a given number of times in each codeword. Upper and lower bounds on the size of such codes under the Hamming metric are discussed, where the lower bounds follow from constructions of good codes. Some of the results are obtained by explicitly finding codes by computer search. A table of exact values and best known bounds on the maximum size for codes of length at most 10 is presented.

We consider the problem of determining the maximum size of a ternary code with constant composition and Hamming weight three. We give several constructions of codes having maximum size and we also present an improvement of the Johnson (1962) bound. The results presented solve the problem for all lengths when d=3, as well as for lengths 7, 11, and all even lengths when d=4.

We derive a lower bound for ternary constant-weight codes with minimum Hamming distance three. The bound is similar to a bound for binary constant-weight codes with minimum distance four described by Graham and Sloane (1980). It improves upon the Gilbert (1952) bound and coincides asymptotically with the Johnson (1962) bound for fixed weight as the codeword length tends to infinity.