Geodesic
On the linear disjunctive decomposition of a $p$-logic function into a product of functions
Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 153-171
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Let $p$ be a prime number, $p\ge 3$. We consider the set of decompositions of a $p$-logic function into a product of functions with disjoint subsets of variables obtained by means of linear substitutions of arguments. Each decomposition of this kind is associated with a decomposition of the vector space into a direct sum of subspaces. We present conditions under which such space decomposition is unique up to rearrangement of subspaces. Also, a criterion for such product to be balanced is given.
Keywords: $p$-logic function, decomposition into a direct product, linear transform. 
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A. V. Cheremushkin. On the linear disjunctive decomposition of a $p$-logic function into a product of functions. Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 153-171. http://geodesic.mathdoc.fr/item/DM_2021_33_4_a12/

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