Suchergebnisse

[EN] We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes. These results demonstrate that there is a lot more scope for constructing self-orthogonal AG codes than was previously known. ; G. McGuire was partially supported by Science Foundation Ireland Grant 13/IA/1914. The remainder authors were partially supported by the Spanish Government and the EU funding program FEDER, Grants MTM2015-65764-C3-2-P and PGC2018-096446-B-C22. F. Hernando and J. J. Moyano-Fernandez are also partially supported by Universitat Jaume I, Grant UJI-B2018-10. ; Hernando, F.; Mcguire, G.; Monserrat Delpalillo, FJ.; Moyano-Fernández, JJ. (2020). Quantum codes from a new construction of self-orthogonal algebraic geometry codes. Quantum Information Processing. 19(4):1-25. https://doi.org/10.1007/s11128-020-2616-8 ; S ; 1 ; 25 ; 19 ; 4 ; Abhyankar, S.S.: Irreducibility criterion for germs of analytic functions of two complex variables. Adv. Math. 74, 190–257 (1989) ; Abhyankar, S.S.: Algebraic Geometry for Scientists and Engineers. Mathematical Surveys and Monographs, American Mathematical Society, Providence (1990) ; Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection I: statement of the problem. IEEE Trans. Inf. Theory 46, 778–788 (2000) ; Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection II: bounds. IEEE Trans. Inf. Theory 46, 789–800 (2000) ; Ashikhmin, A., Knill, E.: Non-binary quantum stabilizer codes. IEEE Trans. Inf. Theory 47, 3065–3072 (2001) ; Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997) ; Bierbrauer, J., Edel, Y.: Quantum twisted codes. J. Comb. Des. 8, 174–188 (2000) ; Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction and orthogonal geometry. Phys. Rev. Lett. 76, 405–409 (1997) ; Calderbank, A.R., Shor, P.W.: Good quantum ...