Weak and strong orders of linear recurring sequences

2017 ◽  
Vol 37 (3) ◽  
pp. 3539-3561
Author(s):  
Zenonas Navickas ◽  
Minvydas Ragulskis ◽  
Dovile Karaliene ◽  
Tadas Telksnys
Keyword(s):  
Linear Recurring Sequences

scholarly journals Equidistribution of linear recurring sequences in finite fields

1977 ◽  
Vol 80 (5) ◽  
pp. 397-405 ◽  
Author(s):  
Harald Niederreiter ◽  
Jau-Shyong Shiue
Keyword(s):  
Finite Fields ◽  
Linear Recurring Sequences

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

2017 ◽  
Vol 9 (3) ◽  
pp. 8
Author(s):  
Yasanthi Kottegoda
Keyword(s):  
Quadratic Form ◽  
Finite Field ◽  
Characteristic Polynomial ◽  
Finite Fields ◽  
Quadratic Forms ◽  
Linear Recurring Sequences ◽  
Exact Number ◽  
Number Of Zeros ◽  
Homogeneous Linear ◽  
Form Approach

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.

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