Some new results on Generalized Algebraic Geometric (GAG) codes are obtained. First, we provide some constructions which significantly improve the general lower bounds on the minimum distance of a GAG code. GAG codes associated to specific maximal curves over finite fields are then investigated. As a result, 2895 improvements on MinT's tables are obtained. Finally, we construct asymptotically good GAG codes with better parameters with respect to those constructed by Spera in 2005. Maximal curves play a role in this context as well.
Generalized algebraic geometric codes from maximal curves
FAINA, Giorgio;
2012
Abstract
Some new results on Generalized Algebraic Geometric (GAG) codes are obtained. First, we provide some constructions which significantly improve the general lower bounds on the minimum distance of a GAG code. GAG codes associated to specific maximal curves over finite fields are then investigated. As a result, 2895 improvements on MinT's tables are obtained. Finally, we construct asymptotically good GAG codes with better parameters with respect to those constructed by Spera in 2005. Maximal curves play a role in this context as well.File in questo prodotto:
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