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On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$

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  • We study the dual linear code of points and generators on a non-singular Hermitian variety $\mathcal{H}(2n+1,q^2)$. We improve the earlier results for $n=2$, we solve the minimum distance problem for general $n$, we classify the $n$ smallest types of code words and we characterize the small weight code words as being a linear combination of these $n$ types.
    Mathematics Subject Classification: Primary: 51E20, 51E22; Secondary: 05B25, 94B05.


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