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arXiv · 2607.19842

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

José Sánchez Menchén·Dan Schwarz·Sally Brouhard·Jacob Martin·Beckett Rebele-Henry·Sammie Ritchie
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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 $\mathbb{F}_{2^6}^{+}\times\mathbb{Z}_4^4$, $\mathbb{Z}_4^4\times\mathbb{F}_{2^{10}}^{+}$, $\mathbb{F}_{2^{10}}^{+}\times\mathbb{Z}_8^4$, $\mathbb{Z}_8^4\times\mathbb{F}_{2^{14}}^{+}$, and $\mathbb{Z}_4^4\times\mathbb{Z}_{16}^2$. 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.

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José Sánchez Menchén, Dan Schwarz, Sally Brouhard, Jacob Martin, Beckett Rebele-Henry, Sammie Ritchie. 2026-07-22. Negative Latin-Square-Type Partial Difference Sets in Non-Elementary Abelian 2-Groups. https://arxiv.org/abs/2607.19842

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