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

Charles J. Colbourn, Sufang Zhao

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)219-227
Number of pages9
JournalDesigns, Codes, and Cryptography
Issue number3
StatePublished - Jul 2000
Externally publishedYes


  • Kirkman triple system
  • Resolvable design
  • Signal set
  • Steiner triple system

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics


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