Necessary and sufficient conditions are determined for two of Bose's constructions of difference families in ${\rm GF}(q)$. These result in new difference families with $\lambda =1$ for block size 4 and orders $p^{2\alpha}$ when $p\equiv 2\pmod 3$ is a prime and $\alpha \geq 1$, and for block size $5$ and orders $p^{4\alpha}$ when $p\equiv 2,3\pmod 5$ is a prime and $\alpha \geq 1$

### Improving two theorems of Bose on difference families

#### Abstract

Necessary and sufficient conditions are determined for two of Bose's constructions of difference families in ${\rm GF}(q)$. These result in new difference families with $\lambda =1$ for block size 4 and orders $p^{2\alpha}$ when $p\equiv 2\pmod 3$ is a prime and $\alpha \geq 1$, and for block size $5$ and orders $p^{4\alpha}$ when $p\equiv 2,3\pmod 5$ is a prime and $\alpha \geq 1$
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654687
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