An asymptotic formula for the number of irreducible transformation shift registers
classification
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irreduciblenumberregistersshifttransformationasymptoticformulacarlitz
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We consider the problem of enumerating the number of irreducible transformation shift registers. We give an asymptotic formula for the number of irreducible transformation shift registers in some special cases. Moreover, we derive a short proof for the exact number of irreducible transformation shift registers of order two using a recent generalization of a theorem of Carlitz.
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