### Abstract

Considering the set H of all linear (or affine) transformations between two vector spaces over a finite field F, the ability of H as a class of hash functions is studied. Hashing a set S of size n into a range, having the same cardinality n by a randomly chosen function from H and looking at the size of the largest hash bucket, is particularly evaluated. If the finite field F has n elements, then there is a bad set S⊂F^{2} of size n with expected minimal bucket size Ω(n^{1/3}). If n is a perfect square there is a worse set with largest bucket size always at least √n. If however, the considered is the field of two elements then better bounds will be obtained. The best previously known upper bound was O(2^{√log n}). This upper bound is reduced to θ(log n/log log n).

Original language | English |
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Pages (from-to) | 465-474 |

Number of pages | 10 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

Publication status | Published - Jan 1 1997 |

Event | Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA Duration: May 4 1997 → May 6 1997 |

### ASJC Scopus subject areas

- Software

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## Cite this

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*, 465-474. https://doi.org/10.1145/258533.258639