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

Authors

S. B. Damelin, Georgia Southern UniversityFollow
Grzegorz J. Michalski, Georgia Southern UniversityFollow
Gary L. Mullen, The Pennsylvania State UniversityFollow

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 Ind_q(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 Ind_q(n, k) = n + 1. We conclude with some pertinent remarks re applications of our results to codes, graphs and hypercubes.

Recommended Citation

Damelin, S. B., Grzegorz J. Michalski, Gary L. Mullen. 2007. "The Cardinality of Sets of k-Independent Vectors over Finite Fields." Monatshefte fur Mathematik, 150 (4): 289-295. doi: 10.1007/s00605-006-0440-6
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/6