A note on the minimal polynomial of the product of linear recurring sequences


Cakcak E.

5th International Conference on Finite Fields and Applications, Augsburg, Almanya, 2 - 06 Ağustos 1999, ss.57-69 identifier

  • Basıldığı Şehir: Augsburg
  • Basıldığı Ülke: Almanya
  • Sayfa Sayıları: ss.57-69

Özet

Let F be a field of nonzero characteristic, with its algebraic closure, 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 sigma and tau in F ($) over bar, 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.