Geodesic
On the existence of certain cyclic difference families and difference matrices
Matematičeskie zametki, Tome 52 (1992) no. 1, pp. 114-119.

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A theorem is proved to the effect that if there exists a $BIB$-schema with parameters $(p^m-1,k,k-1)$, where $k|(p^m-1)$, $p$ is prime, and $m$ is a natural number, then there exists a $BIB$-schema $(p^{mn}-1,k,k-1)$. A consequence is the existnece of a cyclic $BIB$-schema $(p^{mn}-1,p^m-1,p^m-2)$ (($p^m-1$ is prime) that specifies each ordered pair of difference elements at any distance $\rho=1,2,\dots,p^m-2$ (cyclically) precisely once. Recursive theorems on the existence of difference matrices and $(\nu,k,k)$-difference families in the group $Z_v$ of residue classes mod v are proved, along with a theorem on difference families in an additive abelian group. 
@article{MZM_1992_52_1_a15,
     author = {B. T. Rumov},
     title = {On the existence of certain cyclic difference families and difference matrices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {114--119},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1992_52_1_a15/}
}
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B. T. Rumov. On the existence of certain cyclic difference families and difference matrices. Matematičeskie zametki, Tome 52 (1992) no. 1, pp. 114-119. http://geodesic.mathdoc.fr/item/MZM_1992_52_1_a15/