scholarly journals Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil

2002 ◽  
pp. 269-291
Author(s):  
Sudhir R. Ghorpade ◽  
Gilles Lachaud
Keyword(s):  
Finite Fields ◽  
Number Of Solutions ◽  
Solutions Of Equations

scholarly journals Solutions of equations over finite fields: Enumeration via bijections

2016 ◽  
Vol 15 (07) ◽  
pp. 1650136 ◽  
Author(s):  
Ioulia N. Baoulina
Keyword(s):  
Recent Result ◽  
Finite Fields ◽  
Simple Proof ◽  
Character Sums ◽  
Alternative Proof ◽  
Number Of Solutions ◽  
Combinatorial Argument ◽  
Solutions Of Equations

We present a simple proof of the well-known fact concerning the number of solutions of diagonal equations over finite fields. In a similar manner, we give an alternative proof of the recent result on generalizations of Carlitz equations. In both cases, the use of character sums is avoided by using an elementary combinatorial argument.

On the Number of Zeros Over a Finite Field of Certain Symmetric Polynomials

1980 ◽  
Vol 23 (3) ◽  
pp. 327-332
Author(s):  
P. V. Ceccherini ◽  
J. W. P. Hirschfeld
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Polynomial Equations ◽  
Symmetric Polynomials ◽  
Number Of Solutions ◽  
Number Of Zeros

A variety of applications depend on the number of solutions of polynomial equations over finite fields. Here the usual situation is reversed and we show how to use geometrical methods to estimate the number of solutions of a non-homogeneous symmetric equation in three variables.

Power trace functions over finite fields

2019 ◽  
Vol 19 (10) ◽  
pp. 2050196
Author(s):  
Robert W. Fitzgerald ◽  
Yasanthi Kottegoda
Keyword(s):  
Finite Fields ◽  
Trace Function ◽  
Authentication Code ◽  
Number Of Solutions ◽  
Successful Attack

We count the number of solutions to a power trace function equal to a constant and use this to find the probability of a successful attack on an authentication code proposed by Ding et al. (2005) [C. Ding, A. Salomaa, P. Solé and X. Tian, Three constructions of authentication/secrecy codes, J. Pure Appl. Algebra 196 (2005) 149–168].

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