Geodesic
On the existence of Agievich-primitive partitions
Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 4, pp. 104-123

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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 $\mathbf{F}_q^n$ 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, bound, bent function, coordinate subspace, associative block design.
Mots-clés : partition of a space, face 
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     title = {On the existence of {Agievich-primitive} partitions},
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Yu. V. Tarannikov. On the existence of Agievich-primitive partitions. Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 4, pp. 104-123. http://geodesic.mathdoc.fr/item/DA_2022_29_4_a5/