In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all Fq2-rational points of the curve is determined; the Feng-Rao designed minimum distance is computed for infinite families of such codes, as well as the automorphism group. As a result, some linear codes with better relative parameters with respect to one-point Hermitian codes are discovered. Classes of quantum and convolutional codes are provided relying on the constructed AG codes.
Bartoli, D., Montanucci, M., Zini, G. (2018). AG codes and AG quantum codes from the GGS curve. DESIGNS, CODES AND CRYPTOGRAPHY, 86(10), 2315-2344 [10.1007/s10623-017-0450-5].
AG codes and AG quantum codes from the GGS curve
Zini, G
2018
Abstract
In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all Fq2-rational points of the curve is determined; the Feng-Rao designed minimum distance is computed for infinite families of such codes, as well as the automorphism group. As a result, some linear codes with better relative parameters with respect to one-point Hermitian codes are discovered. Classes of quantum and convolutional codes are provided relying on the constructed AG codes.
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