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Volume 29, No 4, 2022, P. 104-123
UDC 519.115.5
Yu. V. Tarannikov
On the existence of Agievich-primitive partitions
Abstract:
We prove that for any positive integer $m$ there exists the smallest positive integer $N = N_{q}(m)$ such that for $n > N$ there are no Agievich-primitive partitions of the space $F_q^n$ into $q^m$ affine subspaces of dimension $n - m$. We give lower and upper bounds on the value $N_{q}(m)$ and prove that $N_{q}(2) = q + 1$. Results of the same type for partitions into coordinate subspaces are established.
Bibliogr. 16.
Keywords: affine subspace, partition of a space, bound, bent function, coordinate subspace, face, associative block design.
DOI: 10.33048/daio.2022.29.747
Yuriy V. Tarannikov 1,2
1. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics,
1 Leninskie Gory, 119991 Moscow, Russia
2. Moscow Center for Fundamental and Applied Mathematics,
1 Leninskie Gory, 119991 Moscow, Russia
e-mail: yutarann@gmail.com
Received July 11, 2022
Revised July 28, 2022
Accepted July 28, 2022
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