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

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

Research output: Contribution to journalArticle

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)289-295
Number of pages7
JournalMonatshefte fur Mathematik
Volume150
Issue number4
DOIs
StatePublished - Apr 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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