On the singularity of generalised Vandermonde matrices over finite fields

Igor E. Shparlinski

doi:10.1016/j.ffa.2004.11.001

On the singularity of generalised Vandermonde matrices over finite fields

Igor E. Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 (λ_i^uj)_i,j=1 ^m, where λ(inf)1(/inf),...,λ(inf)m(/inf) ∈ F_q* are fixed nonzero elements, taken over all (q - 1)^m integer m-tuples (u₁,...,u_m) ∈ [0, q - 2]^m.

Original language	English
Pages (from-to)	193-199
Number of pages	7
Journal	Finite Fields and their Applications
Volume	11
Issue number	2
DOIs	https://doi.org/10.1016/j.ffa.2004.11.001
Publication status	Published - Apr 2005

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title = "On the singularity of generalised Vandermonde matrices over finite fields",

abstract = "We use an upper bound on the number of zeros of sparse polynomials over a finite field Fq to estimate the number of singular matrices of the form (λiuj)i,j=1 m, where λ(inf)1(/inf),...,λ(inf)m(/inf) ∈ Fq* are fixed nonzero elements, taken over all (q - 1)m integer m-tuples (u1,...,um) ∈ [0, q - 2]m.",

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AB - We use an upper bound on the number of zeros of sparse polynomials over a finite field Fq to estimate the number of singular matrices of the form (λiuj)i,j=1 m, where λ(inf)1(/inf),...,λ(inf)m(/inf) ∈ Fq* are fixed nonzero elements, taken over all (q - 1)m integer m-tuples (u1,...,um) ∈ [0, q - 2]m.

UR - https://www.scopus.com/pages/publications/15544367208

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DO - 10.1016/j.ffa.2004.11.001

M3 - Article

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SP - 193

EP - 199

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

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On the singularity of generalised Vandermonde matrices over finite fields

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