Negative Latin-Square-Type Partial Difference Sets in Non-Elementary Abelian 2-Groups

2026/07/22 by José Sánchez Menchén, Dan Schwarz, Sally Brouhard +3
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Abstract

Using cubic cyclotomic classes, character theory, and product constructions motivated by generalized Denniston partial difference sets, we construct negative Latin-square-type partial difference sets in \mathbbF26+×ℤ44, ℤ44×\mathbbF210+, \mathbbF210+×ℤ84, ℤ84×\mathbbF214+, and ℤ44×ℤ162. The first four constructions replace cubic cyclotomic partitions by partitions of non-elementary abelian 2-groups having the same character-value patterns. To the best of our knowledge, these are the first partial difference sets with the stated parameters in the indicated groups.

Related

• Negative Latin square type partial difference sets in nonelementary abelian 2-groups
• New necessary conditions for (negative) Latin square type partial difference sets in abelian groups
• Negative Latin Square Type Partial Difference Sets in Nonabelian Groups of Order 64
• Non-existence of two types of partial difference sets
• Packings of partial difference sets