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A Note on the Minimal Polynomial of the Product of Linear Recurring Sequences

In: Finite Fields and Applications

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  • Emrah Çakçak

    (Middle East Technical University, Department of Mathematics)

Abstract

Let F be a field of nonzero characteristic, with its algebraic closure, $$ \bar{F} $$ . For positive integers a, b, let J (a, b) be the set of integers k, such that (x −1) k is the minimal polynomial of the termwise product of linear recurring sequences σ and τ in $$ \bar{F} $$ , with minimal polynomials (x−1) a and (x−1) b respectively. This set plays a crucial role in the determination of the product of linear recurring sequences with arbitrary minimal polynomials. Here, we give an explicit formula to determine some of the elements of J (a, b), in the case of characteristic 2. We also give some clues for the extension to arbitrary characteristic. The method given here has produced a family of matrices which are themselves interesting.

Suggested Citation

  • Emrah Çakçak, 2001. "A Note on the Minimal Polynomial of the Product of Linear Recurring Sequences," Springer Books, in: Dieter Jungnickel & Harald Niederreiter (ed.), Finite Fields and Applications, pages 57-69, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56755-1_6
    DOI: 10.1007/978-3-642-56755-1_6
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