Article Contents

2011, Volume 5, Issue 3: 489-504. Doi: 10.3934/amc.2011.5.489

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On the order bounds for one-point AG codes

1.
Department of Mathematical Sciences, Aalborg University, Fr. Bajersvej 7G, 9220 Aalborg Øst
2.
Department of Applied Mathematics, University of Valladolid, Avda Salamanca SN, 47014 Valladolid, Castilla
3.
Department of Mathematical Sciences, Aalborg University, Fr. Bajersvej 7G, 9220-Aalborg Øst
4.
Institute of Mathematics, Statistics and Computer Science, P.O. Box 6065, University of Campinas, 13083-970, Campinas, SP

Received: November 2010

Revised: November 2010

Published: August 2011

Abstract / Introduction Related Papers Cited by

Abstract

The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance of general linear codes, and for codes from order domains in particular, was given in [1]. Here we investigate in detail the application of that bound to one-point algebraic geometry codes, obtaining a bound d^* for the minimum distance of these codes. We establish a connection between d^* and the order bound and its generalizations. We also study the improved code constructions based on d^*. Finally we extend d^* to all generalized Hamming weights.

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Mathematics Subject Classification: Primary: 94B27; Secondary: 14G50, 14H55.

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References

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