Abstract
A generalized balanced tournament design, or a GBTD(k, m) in short, is a (km, k, k − 1)-BIBD defined on a km-set V. Its blocks can be arranged into an m × (km − 1) array in such a way that (1) every element of V is contained in exactly one cell of each column, and (2) every element of V is contained in at most k cells of each row. In this paper, we present a new construction for GBTDs and show that a GBTD(4, m) exists for any integer m ≥ 5 with at most eight possible exceptions. A link between a GBTD(k, m) and a near constant composition code is also mentioned. The derived code is optimal in the sense of its size.
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Communicated by C.J. Colbourn.
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Yin, J., Yan, J. & Wang, C. Generalized balanced tournament designs and related codes. Des. Codes Cryptogr. 46, 211–230 (2008). https://doi.org/10.1007/s10623-007-9154-6
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DOI: https://doi.org/10.1007/s10623-007-9154-6