### Abstract

Let f ∈ F_{q}[cursive Greek chi] where F_{q} is a finite field of characteristic p. Wan et al discovered a lower bound for the value set of f in terms of an invariant u_{q}(f) associated to the polynomial f. We define a notion of u_{q}-sharp subsets of F_{q} and discuss related problems. We show how the notion of u_{q}-sharp sets may be used to give yet another proof of the classical Cauchy-Davenport theorem.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Gary L. Mullen, Alain Poli, Henning Stichtenoth |

Publisher | Springer Verlag |

Pages | 249-253 |

Number of pages | 5 |

ISBN (Print) | 9783540213246 |

DOIs | |

State | Published - 2004 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2948 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Das, P. (2004). U

_{q}-sharp subsets of a finite field. In G. L. Mullen, A. Poli, & H. Stichtenoth (Eds.),*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 249-253). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2948). Springer Verlag. https://doi.org/10.1007/978-3-540-24633-6_18