Peculiar Properties of the p-Linear Decomposition of p-Linear Functions in Terms of the Shift-Composition Operation

We analyze the shift-composition operation on discrete functions which occurs under homomorphisms of finite shift registers. We prove that for a prime p , in the class of all functions that are linear in the extreme variables, the notions of reducibility and p -linear reducibility coincide for p -linear functions. Furthermore, we show that a linear function irreducible in the class of all linear functions has no p -linear divisors that are bijective in the rightmost variable, and in some cases, has no p -linear divisors at all.