Exact solutions to Waring's problem for finite fields

  title={Exact solutions to Waring's problem for finite fields},
  author={Arne Winterhof and Christiaan E. van de Woestijne},
  journal={Acta Arithmetica},
with xi ∈ Fq, i.e., as a sum of kth powers of elements of Fq. We can then define the Waring function g(k, q) as the maximal number of summands needed to express all elements of Fq as sums of kth powers. We note that, by an easy argument, we have g(k, q) = g(k, q), where k = gcd(k, q − 1). Hence, we will assume from now on that k divides q − 1. Several authors have established bounds on the value of g(k, q) for various choices of the parameters k and q – a survey is given in [8]. For the cases… 
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Algebraic coding theory
  • E. Berlekamp
  • Computer Science
    McGraw-Hill series in systems science
  • 1968
This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering
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  • Computer Science, Mathematics
    Discret. Appl. Math.
  • 1985
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Covering radius, in: Handbook of coding theory
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  • 1998
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  • Arne Winterhof Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstraße
  • 2009
Covering Codes
On Waring's problem in finite fields
On Waring's problem in finite fields, Acta Arith
  • On Waring's problem in finite fields, Acta Arith
  • 1998