Generalized Algebraic Geometric Codes From Maximal Curves

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 2012-04, Vol.58 (4), p.2386-2396
Main Authors: Calderini, M., Faina, G.
Format: Article
Language:English
Subjects:
AG codes
Algebra
Applied sciences
Asymptotic methods
asymptotically goood codes
Bismuth
Codes
Coding, codes
Entropy
Exact sciences and technology
GAG codes
Indexes
Information theory
Information, signal and communications theory
Linear code
maximal curves
Polynomials
Signal and communications theory
Telecommunications and information theory
Vectors
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2177068