In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdón–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernández.
On certain self-orthogonal AG codes with applications to Quantum error-correcting codes / Bartoli, D.; Montanucci, M.; Zini, G.. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 89:6(2021), pp. 1221-1239. [10.1007/s10623-021-00870-y]
On certain self-orthogonal AG codes with applications to Quantum error-correcting codes
Zini G.
2021
Abstract
In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdón–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernández.
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