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On the linear disjunctive decomposition of a $p$-logic function into a product of functions

A. V. Cheremushkin

Research Institute "Kvant", Moscow

Abstract: 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.

UDC: 519.719.325

Received: 21.06.2021

DOI: 10.4213/dm1650

 English version: Discrete Mathematics and Applications, 2025, 35:1, 1–14

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