Boolean functions constructed using digital sequences of linear recurrences

A class of Boolean functions constructed from digital sequences of linear recurrences over the ring <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi mathvariant="double-struck">Z</m:mi> </m:mrow> <m:mrow> <m:msup> <m:mn>2</m:mn> <m:mi>n</m:mi> </m:msup> </m:mrow> </m:msub> </m:math> Z2ⁿ is considered. We investigate distances between functions, the cardinality of the class, nonlinearity and weights of functions. It is shown that this class consists of functions that are rather distant from the class of all affine functions.