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.

中文翻译：

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p-线性函数的p-线性分解的奇异性质（按移位合成运算）

我们分析了在有限移位寄存器的同态下发生的离散函数的移位合成运算。我们证明，对于素数p，在极端变量中线性的所有函数的类中，可归约性和p-线性可约性的概念与p-线性函数一致。此外，我们证明了在所有线性函数类别中不可约的线性函数没有在最右边变量中双射的p线性除数，并且在某些情况下根本没有p线性除数。