Pless (1972) defines symmetry codes over the field of three elements, called the Pless symmetry codes, and shows that some of these codes yield 5-designs. In this article, we generalize the construction of mutually disjoint Steiner systems studied in Jimbo and Shiromoto (2009) to 5-designs related to a certain class of Pless symmetry codes. As a consequence, we derive new simple 5-designs from the construction.
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Angata, M., Shiromoto, K. Mutually Disjoint 5-Designs From Pless Symmetry Codes. J Stat Theory Pract 6, 78–87 (2012). https://doi.org/10.1080/15598608.2012.647525
- Pless symmetry code
- Self-dual code
- Simple 5-design