Maximum Kirkman Signal Sets for Synchronous Uni-Polar Multi-User Communication Systems

A unipolar signaling system transmits using intensity or amplitude in multiple dimensions. Typical examples arise in optical transmission or radio communication using MT-MFSK as both the signaling and the modulation technique. There are υ dimensions which represent pulses or tones. Each codeword consists of a selection of k of these tones with unit intensity. Each user is assigned m of these binary codewords. In a synchronous multi-user environment, two codewords assigned to a single user have distance 2k, while two codewords assigned to different users have distance at least 2k - 2. Such an assignment of codewords to users is called a Kirkman signal set when the number of users accommodated is the maximum. In this paper, the existence of Kirkman signal sets with k = 3 and m as large as possible is settled for all values of υ.