Quadratic form Approach for the Number of Zeros of Homogeneous Linear Recurring Sequences over Finite Fields

Yasanthi Kottegoda

Journal of Mathematics Research, 2017, vol. 9, issue 3, 8-13

Abstract: We consider homogeneous linear recurring sequences over a finite field $\mathbb{F}_{q}$, based on an irreducible characteristic polynomial of degree $n$ and order $m$. Let $t=(q^{n}-1)/ m$. We use quadratic forms over finite fields to give the exact number of occurrences of zeros of the sequence within its least period when $t$ has q-adic weight 2. Consequently we prove that the cardinality of the set of zeros for sequences from this category is equal to two.

Keywords: Linear recurring sequences; quadratic forms; finite fields (search for similar items in EconPapers)
Date: 2017
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