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arXiv · 2303.17525

On the generalized Fibonacci sequence of polynomials over finite fields

Zekai Chen·Min Sha·Chen Wei
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Abstract

In this paper, as an analogue of the integer case, we study detailedly the period and the rank of the generalized Fibonacci sequence of polynomials over a finite field modulo an arbitrary polynomial. We establish some formulas to compute them, and we also obtain some properties about the quotient of the period and the rank. We find that the polynomial case is much more complicated than the integer case.

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Zekai Chen, Min Sha, Chen Wei. 2023-03-30. On the generalized Fibonacci sequence of polynomials over finite fields. https://arxiv.org/abs/2303.17525

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