The number of polynomials of a given degree over a finite field with value sets of a given cardinality

Pinaki Das

doi:10.1016/S1071-5797(02)00020-5

The number of polynomials of a given degree over a finite field with value sets of a given cardinality

Pinaki Das

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let V_f denote the value set (image) of a polynomial f ε F_q[x]. We relate the number of polynomials f ∈ F_q[x] of degree q - 1 such that V_f = k to the solutions (x_l,...,x_k) of a linear equation over F_q, with the added restriction that x_i≠x_j whenever i≠j. Using this we find a simple formula for the number of such polynomials.

Original language	English (US)
Pages (from-to)	168-174
Number of pages	7
Journal	Finite Fields and their Applications
Volume	9
Issue number	2
DOIs	https://doi.org/10.1016/S1071-5797(02)00020-5
State	Published - Apr 2003

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

Access to Document

10.1016/S1071-5797(02)00020-5

Cite this

@article{0c88348852164c3d875959600cc27848,

title = "The number of polynomials of a given degree over a finite field with value sets of a given cardinality",

abstract = "Let Vf denote the value set (image) of a polynomial f ε Fq[x]. We relate the number of polynomials f ∈ Fq[x] of degree q - 1 such that Vf = k to the solutions (xl,...,xk) of a linear equation over Fq, with the added restriction that xi≠xj whenever i≠j. Using this we find a simple formula for the number of such polynomials.",

author = "Pinaki Das",

year = "2003",

month = apr,

doi = "10.1016/S1071-5797(02)00020-5",

language = "English (US)",

volume = "9",

pages = "168--174",

journal = "Finite Fields and their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - The number of polynomials of a given degree over a finite field with value sets of a given cardinality

AU - Das, Pinaki

PY - 2003/4

Y1 - 2003/4

N2 - Let Vf denote the value set (image) of a polynomial f ε Fq[x]. We relate the number of polynomials f ∈ Fq[x] of degree q - 1 such that Vf = k to the solutions (xl,...,xk) of a linear equation over Fq, with the added restriction that xi≠xj whenever i≠j. Using this we find a simple formula for the number of such polynomials.

AB - Let Vf denote the value set (image) of a polynomial f ε Fq[x]. We relate the number of polynomials f ∈ Fq[x] of degree q - 1 such that Vf = k to the solutions (xl,...,xk) of a linear equation over Fq, with the added restriction that xi≠xj whenever i≠j. Using this we find a simple formula for the number of such polynomials.

UR - http://www.scopus.com/inward/record.url?scp=0037396636&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037396636&partnerID=8YFLogxK

U2 - 10.1016/S1071-5797(02)00020-5

DO - 10.1016/S1071-5797(02)00020-5

M3 - Article

AN - SCOPUS:0037396636

SN - 1071-5797

VL - 9

SP - 168

EP - 174

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

IS - 2

ER -

The number of polynomials of a given degree over a finite field with value sets of a given cardinality

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this