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On the propagation criterion for Boolean functions and on bent functions. (English. Russian original) Zbl 1037.94560
Probl. Inf. Transm. 33, No. 1, 62-71 (1997); translation from Probl. Peredachi Inf. 33, No. 1, 75-86 (1997).
Summary: We consider the parameters of a Boolean function that characterize its position relative to the first-order Reed-Muller $$R(1,n)$$-code. We establish simple criteria for a given vector, for a given Boolean function, to be unessential, to be a linear structure, or to belong to $$\mathbb{P} C(f)$$. We find conditions under which the set $$\mathbb{P} C(f)$$ contains a linear subspace (without zero), and we show that the greater the dimension of the subspace, the more distant such are functions from $$R(1,n)$$. We obtain a new description of the class of bent functions that are the most remote from $$R(1,n)$$.

##### MSC:
 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010) 94B99 Theory of error-correcting codes and error-detecting codes