On the singularity of generalised Vandermonde matrices over finite fields

Authors:
Igor E. Shparlinski
Affiliations:
Department of Computing, Macquarie University, North Ryde, Sydney, NSW 2109, Australia
Venue:
Finite Fields and Their Applications
Year:
2005

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Abstract

We use an upper bound on the number of zeros of sparse polynomials over a finite field F"q to estimate the number of singular matrices of the form (@l"i^u^"^j)"i","j"="1^m, where @l"1,...,@l"m@?F"q^* are fixed nonzero elements, taken over all (q-1)^m integer m-tuples (u"1,...,u"m)@?[0,q-2]^m.