The cardinality of sets of k-independent vectors over finite fields

S. B. Damelin, G. Michalski, Gary L. Mullen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)289-295
Number of pages7
JournalMonatshefte fur Mathematik
Issue number4
StatePublished - Apr 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


Dive into the research topics of 'The cardinality of sets of k-independent vectors over finite fields'. Together they form a unique fingerprint.

Cite this