The Cardinality of Sets of <Emphasis Type="Italic">k</Emphasis>-Independent Vectors over Finite Fields |
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| Authors: | S B Damelin G Michalski Gary L Mullen |
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| Institution: | (1) Georgia Southern University, Statesboro, GA, USA;(2) The Pennsylvania State University, University Park, PA, USA |
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| 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.
Supported, in part by grants EP/C000285, NSF-DMS-0439734 and NSF-DMS-0555839. S. B. Damelin thanks the Institute for Mathematics
and Applications for their hospitality. |
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| Keywords: | 2000 Mathematics Subject Classification: 05B05 05B15 05B25 05B35 94B05 94B65 05C38 15A03 |
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