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Hadamard Partitioned Difference Families and Their Descendants by Buratti, Marco is a scholarly article available to read on EtoBox.

What is Hadamard Partitioned Difference Families and Their Descendants about?

If $D$ is a $(4u^2,2u^2-u,u^2-u)$ Hadamard difference set (HDS) in $G$, then $\{G,G\setminus D\}$ is clearly a $(4u^2,[2u^2-u,2u^2+u],2u^2)$ partitioned difference family (PDF). Any $(v,K,\lambda)$-PDF will be said of Hadamard-type if $v=2\lambda$ as the one above. We present a doubling construction which, starting from any such PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order $4u^2(2n+1)$ and three block-sizes $4u^2-2u$, $4u^2$ and $4u^2+2u$, whenever we have a $(4u^2,2u^2-u,u^2-u)$-HDS and the maximal prime power divisors of $2n+1$ are all greater than $4u^2+2u$.

Author

Buratti, Marco

Published

2017

Language

EN