Title

The Cardinality of Sets of k-Independent Vectors over Finite Fields

Document Type

Article

Publication Date

4-2007

Publication Title

Monatshefte fur Mathematik

DOI

10.1007/s00605-006-0440-6

ISSN

1436-5081

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 Indq(n, k) of a k-independent set of vectors in the n-dimensional vector space F qnover the finite field F qof order q. Namely, we give a necessary and sufficient condition for Indq(n, k) = n + 1. We conclude with some pertinent remarks re applications of our results to codes, graphs and hypercubes.

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