AG codes and AG quantum codes from the GGS curve |
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| Authors: | Daniele Bartoli Maria Montanucci Giovanni Zini |
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| Affiliation: | 1.Dipartimento di Matematica e Informatica,Università degli Studi di Perugia,Perugia,Italy;2.Dipartimento di Matematica Informatica ed Economia,Università degli Studi della Basilicata, Campus di Macchia Romana,Potenza,Italy;3.Dipartimento di Matematica e Informatica,Università degli Studi di Firenze,Firenze,Italy |
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| Abstract: | In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all (mathbb F_{q^2})-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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