Constructions of Nested Partial Difference Sets with Galois Rings |
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Authors: | John B Polhill |
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Institution: | (1) Department of Mathematics, Computer Science, and Statistics, Bloomsburg University of Pennsylvania, Bloomsburg, PA, 17815, U.S.A |
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Abstract: | There have been several recent constructions of partial difference sets (PDSs) using the Galois rings
for p a prime and t any positive integer. This paper presents constructions of partial difference sets in
where p is any prime, and r and t are any positive integers. For the case where
many of the partial difference sets are constructed in groups with parameters distinct from other known constructions, and the PDSs are nested. Another construction of Paley partial difference sets is given for the case when p is odd. The constructions make use of character theory and of the structure of the Galois ring
, and in particular, the ring
×
. The paper concludes with some open related problems. |
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Keywords: | Galois rings difference sets partial difference sets |
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