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This article is cited in 2 scientific papers (total in 2 papers)
A method of constructing generalized difference sets
B. T. Rumov Steklov Mathematical Institute, Academy of Sciences of the USSR
Abstract:
On the elements of the ring of residues modulo $v(2\nmid v,3\nmid v)$ we construct cyclic PBIB-designs with $\tau(v)-1$ classes of connectedness, where $\tau(v)$ is the number of divisors of $v$. We prove the existence of cyclic BIB-designs with parameters $b$, $v$, $r$, $k$ and $\lambda$ such that: 1) $\lambda=k$ (and also $\lambda=k/2$ if $k$ is even), $k\ge4$, and $k-1\mid p-1$ for each prime divisor $p$ of the number $v$; 2) $\lambda=(k-l)/2$, $k$ odd, $k\ge3$, $k\mid p-1$ for each prime divisor $p$ of the number $v$.
Received: 12.04.1973
Citation:
B. T. Rumov, “A method of constructing generalized difference sets”, Mat. Zametki, 15:4 (1974), 551–560; Math. Notes, 15:4 (1974), 324–329
Linking options:
https://www.mathnet.ru/eng/mzm7378 https://www.mathnet.ru/eng/mzm/v15/i4/p551
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Abstract page: | 183 | Full-text PDF : | 75 | First page: | 1 |
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