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

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10.1016/S1071-5797(02)00020-5

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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.",

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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.

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

Abstract

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