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arXiv · 2307.09852

A few more Hadamard Partitioned Difference Families

Anamari Nakic
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Abstract

A $(G,[k_1,\dots,k_t],λ)$ {\it partitioned difference family} (PDF) is a partition $\cal B$ of an additive group $G$ into sets ({\it blocks}) of sizes $k_1$, \dots, $k_t$, such that the list of differences of ${\cal B}$ covers exactly $λ$ times every non-zero element of $G$. It is called {\it Hadamard} (HPDF) if the order of $G$ is $2λ$. The study of HPDFs is motivated by the fact that each of them gives rise, recursively, to infinitely many other PDFs. Apart from the {\it elementary} HPDFs consisting of a Hadamard difference set and its complement, only one HPDF was known. In this article we present three new examples in several groups and we start a general investigation on the possible existence of HPDFs with assigned parameters by means of simple arguments.

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Anamari Nakic. 2023-07-19. A few more Hadamard Partitioned Difference Families. https://arxiv.org/abs/2307.09852

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