### 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) |
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Pages (from-to) | 168-174 |

Number of pages | 7 |

Journal | Finite Fields and their Applications |

Volume | 9 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2003 |

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### 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.

Research output: Contribution to journal › Article

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 - 2003/4/1

Y1 - 2003/4/1

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

VL - 9

SP - 168

EP - 174

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

IS - 2

ER -