Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 649-658
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B. T. Rumov. Constructing block designs of elements or residue rings with a composite modulus. Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 649-658. http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a6/
@article{MZM_1971_10_6_a6,
author = {B. T. Rumov},
title = {Constructing block designs of elements or residue rings with a composite modulus},
journal = {Matemati\v{c}eskie zametki},
pages = {649--658},
year = {1971},
volume = {10},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a6/}
}
TY - JOUR
AU - B. T. Rumov
TI - Constructing block designs of elements or residue rings with a composite modulus
JO - Matematičeskie zametki
PY - 1971
SP - 649
EP - 658
VL - 10
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a6/
LA - ru
ID - MZM_1971_10_6_a6
ER -
%0 Journal Article
%A B. T. Rumov
%T Constructing block designs of elements or residue rings with a composite modulus
%J Matematičeskie zametki
%D 1971
%P 649-658
%V 10
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a6/
%G ru
%F MZM_1971_10_6_a6
The paper provides a construction of cyclic BIB designs with parameters $b, v, r, k$, and $\lambda$ such that $\lambda=k-1$, $k\geqslant3$, and $p\equiv1\pmod{k}$ for each prime divisor $p$ of the number $v$. The existence is proven of bases consisting of $(v-1)/k$ blocks and, for $v=p^\alpha$, this base is given explicitly.
