On the number of zeros to the equation f(x1)+... + f(x)=a over finite fields

2021 ◽  
Vol 76 ◽  
pp. 101922
Author(s):  
Chaoxi Zhu ◽  
Yulu Feng ◽  
Shaofang Hong ◽  
Junyong Zhao
Keyword(s):  
Finite Fields ◽  
Number Of Zeros

scholarly journals Quadratic form Approach for the Number of Zeros of Homogeneous Linear Recurring Sequences over Finite Fields

2017 ◽  
Vol 9 (3) ◽  
pp. 8
Author(s):  
Yasanthi Kottegoda
Keyword(s):  
Quadratic Form ◽  
Finite Field ◽  
Characteristic Polynomial ◽  
Finite Fields ◽  
Quadratic Forms ◽  
Linear Recurring Sequences ◽  
Exact Number ◽  
Number Of Zeros ◽  
Homogeneous Linear ◽  
Form Approach

We consider homogeneous linear recurring sequences over a finite field $\mathbb{F}_{q}$, based on an irreducible characteristic polynomial of degree $n$ and order $m$. Let $t=(q^{n}-1)/ m$. We use quadratic forms over finite fields to give the exact number of occurrences of zeros of the sequence within its least period when $t$ has q-adic weight 2. Consequently we prove that the cardinality of the set of zeros for sequences from this category is equal to two.

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.

scholarly journals Number of Zeros of Diagonal Polynomials over Finite Fields

2001 ◽  
Vol 7 (1) ◽  
pp. 197-204 ◽  
Author(s):  
Ren Debin ◽  
Sun Qi ◽  
Yuan Pingzhi
Keyword(s):  
Finite Fields ◽  
Number Of Zeros ◽  
Polynomials Over Finite Fields

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields

Maximum Distance Separable Hankel Rhotrices over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Maximum Distance ◽  
Maximum Distance Separable

Notes on three-pass protocol

2020 ◽  
Vol 25 (4) ◽  
pp. 4-9
Author(s):  
Yerzhan R. Baissalov ◽  
Ulan Dauyl
Keyword(s):  
Finite Fields ◽  
Matrix Algebras ◽  
Associative Structures

The article discusses primitive, linear three-pass protocols, as well as three-pass protocols on associative structures. The linear three-pass protocols over finite fields and the three-pass protocols based on matrix algebras are shown to be cryptographically weak.

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