Abstract
A decomposition of the blocks of an \(\textsf {STS}(v)\) into partial parallel classes of size m is equivalent to a Kirkman signal set \(\textsf {KSS}(v,m)\). We give decompositions of \(\textsf {STS}(4v-3)\) into classes of size \(v-1\) when \(v \equiv 3 \pmod {6}\), \(v \not = 3\). We also give decompositions of \(\textsf {STS}(v)\) into classes of various sizes when v is a product of two arbitrary integers that are both congruent to \(3 \pmod {6}\). These results produce new families of \(\textsf {KSS}(v,m)\).
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Communicated by C. J. Colbourn.
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Hodaj, J., Keranen, M.S., Kreher, D.L. et al. Some new Kirkman signal sets. Des. Codes Cryptogr. 86, 2183–2195 (2018). https://doi.org/10.1007/s10623-017-0445-2
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DOI: https://doi.org/10.1007/s10623-017-0445-2