TY - JOUR
T1 - Maximum Kirkman Signal Sets for Synchronous Uni-Polar Multi-User Communication Systems
AU - Colbourn, Charles J.
AU - Zhao, Sufang
N1 - Funding Information:
Research of the authors is supported by ARO grant DAAG55-98-1-0272 (Colbourn).
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2000/7
Y1 - 2000/7
N2 - 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.
AB - 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.
KW - Kirkman triple system
KW - Resolvable design
KW - Signal set
KW - Steiner triple system
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U2 - 10.1023/A:1008393607487
DO - 10.1023/A:1008393607487
M3 - Article
AN - SCOPUS:0347372747
SN - 0925-1022
VL - 20
SP - 219
EP - 227
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 3
ER -