scholarly journals Irreducible polynomials with consecutive zero coefficients

2008 ◽  
Vol 14 (1) ◽  
pp. 201-208 ◽  
Author(s):  
Theodoulos Garefalakis
Keyword(s):  
Irreducible Polynomials ◽  
Consecutive Zero

scholarly journals A new class of irreducible polynomials

2021 ◽  
pp. 1-6
Author(s):  
Jitender Singh ◽  
Sanjeev Kumar
Keyword(s):  
Irreducible Polynomials ◽  
New Class

Composite values of irreducible polynomials

2019 ◽  
Vol 74 (1) ◽  
pp. 36-37
Author(s):  
Franz Lemmermeyer
Keyword(s):  
Irreducible Polynomials

scholarly journals Multiplicative groups of fields and hereditarily irreducible polynomials

2016 ◽  
Vol 168 ◽  
pp. 452-471
Author(s):  
Alice Medvedev ◽  
Ramin Takloo-Bighash
Keyword(s):  
Irreducible Polynomials ◽  
Multiplicative Groups

The Number of Irreducible Polynomials and Lyndon Words with Given Trace

2001 ◽  
Vol 14 (2) ◽  
pp. 240-245 ◽  
Author(s):  
F. Ruskey ◽  
C. R. Miers ◽  
J. Sawada
Keyword(s):  
Irreducible Polynomials ◽  
Lyndon Words

Construction of hash functions based on theory of finite fields with the use of irreducible polynomials

2021 ◽  
Vol 143 (2) ◽  
pp. 66-76
Author(s):  
U.K. Turusbekova ◽  
◽  
S.A. Altynbek ◽  
A.S. Turginbayeva ◽  
L. Mereikhan ◽  
...  
Keyword(s):  
Finite Fields ◽  
Hash Functions ◽  
Irreducible Polynomials

Construction of Irreducible Polynomials

1993 ◽  
pp. 39-68
Author(s):  
Ian F. Blake ◽  
XuHong Gao ◽  
Ronald C. Mullin ◽  
Scott A. Vanstone ◽  
Tomik Yaghoobian
Keyword(s):  
Irreducible Polynomials

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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