Irreducible Polynomials

A low complexity bit parallel polynomial basis systolic multiplier for general irreducible polynomials and trinomials

Microelectronics Journal ◽

10.1016/j.mejo.2021.105163 ◽

2021 ◽

pp. 105163

Author(s):

Sakshi Devi ◽

Rita Mahajan ◽

Deepak Bagai

Keyword(s):

Low Complexity ◽

Polynomial Basis ◽

Irreducible Polynomials ◽

Systolic Multiplier

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A new class of irreducible polynomials

Communications in Algebra ◽

10.1080/00927872.2021.1881789 ◽

2021 ◽

pp. 1-6

Author(s):

Jitender Singh ◽

Sanjeev Kumar

Keyword(s):

Irreducible Polynomials ◽

New Class

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Composite values of irreducible polynomials

Elemente der Mathematik ◽

10.4171/em/378 ◽

2019 ◽

Vol 74 (1) ◽

pp. 36-37

Author(s):

Franz Lemmermeyer

Keyword(s):

Irreducible Polynomials

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Multiplicative groups of fields and hereditarily irreducible polynomials

Journal of Number Theory ◽

10.1016/j.jnt.2016.04.020 ◽

2016 ◽

Vol 168 ◽

pp. 452-471

Author(s):

Alice Medvedev ◽

Ramin Takloo-Bighash

Keyword(s):

Irreducible Polynomials ◽

Multiplicative Groups

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The Number of Irreducible Polynomials and Lyndon Words with Given Trace

SIAM Journal on Discrete Mathematics ◽

10.1137/s0895480100368050 ◽

2001 ◽

Vol 14 (2) ◽

pp. 240-245 ◽

Cited By ~ 16

Author(s):

F. Ruskey ◽

C. R. Miers ◽

J. Sawada

Keyword(s):

Irreducible Polynomials ◽

Lyndon Words

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

Vestnik KazNRTU ◽

10.51301/vest.su.2021.i2.09 ◽

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

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Construction of Irreducible Polynomials

Applications of Finite Fields ◽

10.1007/978-1-4757-2226-0_3 ◽

1993 ◽

pp. 39-68

Author(s):

Ian F. Blake ◽

XuHong Gao ◽

Ronald C. Mullin ◽

Scott A. Vanstone ◽

Tomik Yaghoobian

Keyword(s):

Irreducible Polynomials

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On Brown’s constant associated with irreducible polynomials over henselian valued fields

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2010.02.028 ◽

2010 ◽

Vol 214 (12) ◽

pp. 2294-2300 ◽

Cited By ~ 4

Author(s):

Sudesh K. Khanduja

Keyword(s):

Irreducible Polynomials ◽

Valued Fields ◽

Henselian Valued Fields

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Irreducible Polynomials in ℝ[x]

A Concrete Introduction to Higher Algebra - Undergraduate Texts in Mathematics ◽

10.1007/978-1-4684-0065-6_19 ◽

1979 ◽

pp. 142-143

Author(s):

Lindsay Childs

Keyword(s):

Irreducible Polynomials

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Short Kloosterman Sums for Polynomials over Finite Fields

Canadian Journal of Mathematics ◽

10.4153/cjm-2003-010-0 ◽

2003 ◽

Vol 55 (2) ◽

pp. 225-246 ◽

Cited By ~ 1

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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