Modular Golomb rulers and almost difference sets
| Autor: | Gordon, Daniel M. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A $(v,k,\lambda)$-difference set in a group $G$ of order $v$ is a subset $\{d_1, d_2, \ldots,d_k\}$ of $G$ such that $D=\sum d_i$ in the group ring ${\mathbb Z}[G]$ satisfies $$D D^{-1} = n + \lambda G,$$ where $n=k-\lambda$. In other words, the nonzero elements of $G$ all occur exactly $\lambda$ times as differences of elements in $D$. A $(v,k,\lambda,t)$-almost difference set has $t$ nonzero elements of $G$ occurring $\lambda$ times, and the other $v-1-t$ occurring $\lambda+1$ times. When $\lambda=0$, this is equivalent to a modular Golomb ruler. In this paper we investigate existence questions on these objects, and extend previous results constructing almost difference sets by adding or removing an element from a difference set. Comment: 6 pages, 1 figure |
| Databáze: | arXiv |
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