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Irreducible polynomials and linear recurring arrays

✍ Scribed by Liu Mulan; Gary L. Mullen

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
388 KB
Volume
74
Category
Article
ISSN
0166-218X

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✦ Synopsis

For CI E Fq the finite field of order q and b E F,(a), let FJt(,fi) = F,(y). We obtain an explicit formula for the minimal polynomial h?(x) of y in terms of the greatest common divisor of two polynomials which are closely related to the minimal polynomials fl(x) of a and g&) of /I. We also give an application of this result to linear recurring arrays.

πŸ“œ SIMILAR VOLUMES

Polynomial Distribution and Sequences of
Polynomial Distribution and Sequences of Irreducible Polynomials over Finite Fields
✍ Wun-Seng Chou; Stephen D Cohen πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 153 KB

Let k=GF(q) be the finite field of order q. Let f 1 (x), f 2 (x) # k[x] be monic relatively prime polynomials satisfying n=deg f 1 >deg f 2 0 and f 1 (x)Γ‚f 2 (x){ g 1 (x p )Γ‚g 2 (x p ) for any g 1 (x), g 2 (x) # k[x]. Write Q(x)= f 1 (x)+tf 2 (x) and let K be the splitting field of Q(x) over k(t). L