T-user code with arbitrary code length for multiple-access adder channel

A T-user uniquely decodable (UD) code {C-1,C-2,...,C-T} Over an integer set {0, 1,..., k} with arbitrary code length is developed for a multiple-access adder channel (MAAC). Each of the T users is equipped with two codewords, one of which is zero vector. The T-user UD code is used to identify users through the MAAC. It is shown that a T(f+g+1)-user UD code with code length f+g+1 can be arranged from two given T(f)-user and T(g)-user UD codes. This idea makes it possible to construct recursively a T-user UD code for an arbitrary code length n and a positive integer k. The T-user UD code includes the Jevtic code.