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Hermitian forms, trace equations and application to codes

Dany-Jack Mercier
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Abstract

We provide a systematic study of sesquilinear hermitian forms and a new proof of the calculus of some exponential sums defined with quadratic hermitian forms. The computation of the number of solutions of equations such as Tr(f(x)+v.x)=0 or Tr(f(x))=a allows us to construct codes and to obtain their parameters.

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Dany-Jack Mercier. 2003-04-21. Hermitian forms, trace equations and application to codes. https://arxiv.org/abs/math/0111191

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