Products of linear recurring sequences with maximum complexity

1987 ◽  
Vol 33 (1) ◽  
pp. 124-131 ◽  
Author(s):  
R. Rueppel ◽  
O. Staffelbach
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.

Linear recurring sequences over rings and modules

1995 ◽  
Vol 76 (6) ◽  
pp. 2793-2915 ◽  
Author(s):  
V. L. Kurakin ◽  
A. S. Kuzmin ◽  
A. V. Mikhalev ◽  
A. A. Nechaev
Keyword(s):  
Linear Recurring Sequences
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