An asymptotic formula for the number of irreducible transformation shift registers

Abstract

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.

14 pages

References in corpus (2)

• The Splitting Subspace Conjecture
• Enumeration of Linear Transformation Shift Registers

Cited by in corpus (2)

• A note on the multiple-recursive matrix method for generating pseudorandom vectors
• Primitive transformation shift registers over finite fields