Abstract
In 2020, Liu (Q. Liu, The lower bounds on the second-order nonlinearity of three classes of Boolean functions, Advances in Mathematics of Communications, AIMS (2021), Doi: 10.3934/amc.2020136) studied the second-order nonlinearity of three classes of Boolean functions, which have high first-order nonlinearity. Liu gave bounds on the first-order nonlinearity of these classes based on some experimental results using Magma. This article provides theoretical proof for computing the lower bounds on the first-order nonlinearity of two classes of Boolean functions out of three. Our bounds are identical to the bounds obtained by Liu experimentally.
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