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.
AG codes and AG quantum codes from the GGS curve / Bartoli, D.; Montanucci, M.; Zini, G.. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 86:10(2018), pp. 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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