Distribution of Elements on Cycles of Linear Recurrences over Galois Field

A. S. Nelubin

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 534-542 from Springer

Abstract: Abstract Let y be a linear recurring sequence (LRS) over the field P of q = p s elements, which has irreducible characteristic polynomial of degree m and period $$\Delta = \frac{{{q^m} - 1}}{d}$$ where d ∈ Z divides q m − 1 and p t + 1 for some t ∈ N. For this sequence v we described possible frequences of appearance of element a ∈ P in the cycle (v(0), v(1),..., v(Δ − 1)). The proofs are based on properties of Gauss sums and generalize the results of works [2, 3].

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_51

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