### Abstract

A set of vectors is k-independent if all its subsets with no more than k elements are linearly independent. We obtain a result concerning the maximal possible cardinality Ind _{q} (n, k) of a k-independent set of vectors in the n-dimensional vector space F _{q} ^{n} over the finite field F _{q} of order q. Namely, we give a necessary and sufficient condition for Ind _{q} (n, k) = n + 1. We conclude with some pertinent remarks re applications of our results to codes, graphs and hypercubes.

Original language | English (US) |
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Pages (from-to) | 289-295 |

Number of pages | 7 |

Journal | Monatshefte fur Mathematik |

Volume | 150 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2007 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Damelin, S. B., Michalski, G., & Mullen, G. L. (2007). The cardinality of sets of k-independent vectors over finite fields.

*Monatshefte fur Mathematik*,*150*(4), 289-295. https://doi.org/10.1007/s00605-006-0440-6