The Berlekamp-Massey algorithm and linear recurring sequences over a factorial domain

1995 ◽  
Vol 6 (4-5) ◽  
pp. 309-323 ◽  
Author(s):  
Patrick Fitzpatrick ◽  
Graham H. Norton
Keyword(s):  
Linear Recurring Sequences ◽  
Factorial Domain

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.

scholarly journals Recent results on weakly factorial domains

2018 ◽  
Vol 20 ◽  
pp. 01001
Author(s):  
Chang Gyu Whan
Keyword(s):  
Polynomial Ring ◽  
Quotient Group ◽  
Integral Domain ◽  
Laurent Polynomial ◽  
Semigroup Ring ◽  
Prime Element ◽  
Cancellative Monoid ◽  
Factorial Domain ◽  
Laurent Polynomial Ring

In this paper, we will survey recent results on weakly factorial domains base on the results of [11, 13, 14]. LetD be an integral domain, X be an indeterminate over D, d ∈ D, R = D[X,d/X] be a subring of the Laurent polynomial ring D[X,1/X], Γ be a nonzero torsionless commutative cancellative monoid with quotient group G, and D[Γ] be the semigroup ring of Γ over D. Among other things, we show that R is a weakly factorial domain if and only if D is a weakly factorial GCD‐domain and d = 0, d is a unit of D or d is a prime element of D. We also show that if char(D) = 0 (resp., char(D) = p > 0), then D[Γ] is a weakly factorial domain if and only if D is a weakly factorial GCD domain, Γ is a weakly factorial GCD semigroup, and G is of type (0,0,0,…) (resp., (0,0,0,…) except p).

Sign in / Sign up

Export Citation Format

Share Document