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

M. De Boeck; P. Vandendriessche

doi:10.3934/amc.2014.8.281

Article Contents

2014, Volume 8, Issue 3: 281-296. Doi: 10.3934/amc.2014.8.281

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

M. De Boeck^1, and
P. Vandendriessche^1,

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

Received: March 2013

Published: August 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 51E20, 51E22; Secondary: 05B25, 94B05.

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