### Abstract

It is shown that for any t > c_{p}log n linear bases B_{1}, ..., B_{t} of Z_{p}^{n} their union (with repetitions) ∪_{i = 1}^{t} B_{i} forms an additive basis of Z_{p}^{n}; i.e., for any x ε{lunate} Z_{p}^{n} there exist A_{1} ⊃ B_{1}, ..., A_{t} ⊃ B_{t} such that x = Σ_{i = 1}^{t} Σ_{y ε{lunate} Ai} y.

Original language | English (US) |
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Pages (from-to) | 203-210 |

Number of pages | 8 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 57 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1991 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Alon, N., Linial, N., & Meshulam, R. (1991). Additive bases of vector spaces over prime fields.

*Journal of Combinatorial Theory, Series A*,*57*(2), 203-210. https://doi.org/10.1016/0097-3165(91)90045-I