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

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)168-174
Number of pages7
JournalFinite Fields and their Applications
Volume9
Issue number2
DOIs
StatePublished - Apr 1 2003

Fingerprint

Galois field
Cardinality
Polynomials
Polynomial
Linear equations
Linear equation
Denote
Restriction

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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The number of polynomials of a given degree over a finite field with value sets of a given cardinality. / Das, Pinaki.

In: Finite Fields and their Applications, Vol. 9, No. 2, 01.04.2003, p. 168-174.

Research output: Contribution to journalArticle

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