On the order bound for one-point AG codes

The order bound for the minimum distance of algebraic geometry codes is defined for the dual of one-point codes. A new bound for the minimum distance of linear codes, and for codes from order domains in particular, was given in [1]. We investigate in detail the application of that bound to one-point algebraic geometry codes and establish the connection to the order bound. We also establish a connection between the improved code constructions based on the two bounds. The same ideas are applied to all generalized Hamming weights.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Olav Geil, Carlos Munuera, Diego Ruano, Fernando Torres
• Keywords: Algebraic Geometry Codes, CORR 2010, Education, Minimum Distance, One-point Codes