FACTORIZATION OF SOME COMPOSITE POLYNOMIALS OVER FINITE FIELDS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250180
Author(s):  
MAHMOOD ALIZADEH ◽  
MELSIK K. KYUREGYAN
Keyword(s):  
Finite Fields ◽  
Composition Methods ◽  
Polynomial Composition ◽  
Polynomials Over Finite Fields

In this paper we study the factorization of composite polynomials, constructed with some polynomial composition methods, into irreducible factors over finite fields. The main aim of this paper is to provide a proof of a useful theorem of Varshamov (1973), which had been stated by him, without proof.

Construction of primitive polynomials over finite fields

2020 ◽  
pp. 2150078
Author(s):  
Mahmood Alizadeh
Keyword(s):  
Finite Fields ◽  
Primitive Polynomial ◽  
Composition Methods ◽  
Primitive Polynomials ◽  
Polynomial Composition ◽  
Polynomials Over Finite Fields

In this paper, using the polynomial composition methods some computationally simple and explicit ways for constructing higher degrees primitive polynomials from a given primitive polynomial over [Formula: see text] are given.

Some primitive polynomials over finite fields

2001 ◽  
Vol 21 (3) ◽  
pp. 412-416 ◽  
Author(s):  
Seunghwan Chang ◽  
June Bok Lee
Keyword(s):  
Finite Fields ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

scholarly journals Factorization of a class of polynomials over finite fields

2012 ◽  
Vol 18 (1) ◽  
pp. 108-122 ◽  
Author(s):  
Henning Stichtenoth ◽  
Alev Topuzoğlu
Keyword(s):  
Finite Fields ◽  
Polynomials Over Finite Fields

scholarly journals Value sets of polynomials over finite fields

1993 ◽  
Vol 119 (3) ◽  
pp. 711-711 ◽  
Author(s):  
Da Qing Wan ◽  
Peter Jau-Shyong Shiue ◽  
Ching Shyang Chen
Keyword(s):  
Finite Fields ◽  
Polynomials Over Finite Fields ◽  
Value Sets

scholarly journals Short Kloosterman Sums for Polynomials over Finite Fields

2003 ◽  
Vol 55 (2) ◽  
pp. 225-246 ◽  
Author(s):  
William D. Banks ◽  
Asma Harcharras ◽  
Igor E. Shparlinski
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Small Degree ◽  
Kloosterman Sums ◽  
Degree Relative ◽  
Irreducible Polynomials ◽  
Arbitrary Polynomial ◽  
Polynomials Over Finite Fields ◽  
Titchmarsh Theorem

AbstractWe extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring [x]/M(x) for collections of polynomials either of the form f−1g−1 or of the form f−1g−1 + afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields.

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