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August  2014, 8(3): 281-296. doi: 10.3934/amc.2014.8.281

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

 1 UGent, Department of Mathematics, Krijgslaan 281-S22, 9000 Gent, Flanders, Belgium, Belgium

Received  March 2013 Published  August 2014

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.
Citation: M. De Boeck, P. Vandendriessche. On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$. Advances in Mathematics of Communications, 2014, 8 (3) : 281-296. doi: 10.3934/amc.2014.8.281
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