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 language||English (US)|
|Number of pages||7|
|Journal||Monatshefte fur Mathematik|
|State||Published - Apr 2007|
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