On the functional codes arising from the intersections of algebraic hypersurfaces of small degree with a non-singular quadric

Daniele Bartoli; Leo Storme

doi:10.3934/amc.2014.8.271

Article Contents

2014, Volume 8, Issue 3: 271-280. Doi: 10.3934/amc.2014.8.271

This issue Previous Article Higher genus universally decodable matrices (UDMG) Next Article On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$

On the functional codes arising from the intersections of algebraic hypersurfaces of small degree with a non-singular quadric

Daniele Bartoli^1, and
Leo Storme^2,

1.
Dipartimento di Matematica ed Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia
2.
Department of Mathematics, Ghent University, Krijgslaan 281 - S22, 9000 Ghent

Received: January 2013

Revised: January 2014

Published: August 2014

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Abstract

We discuss the functional codes $C_h(\mathcal{Q}_N)$, for small $h\geq 3$, $q>9$, and for $N\geq 6$. This continues the study of different classes of functional codes, performed on functional codes arising from quadrics and Hermitian varieties. Here, we consider the functional codes arising from the intersections of the algebraic hypersurfaces of small degree $h$ with a given non-singular quadric $\mathcal{Q}_N$ in PG$(N,q)$.

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

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References

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