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Quantum codes from a new construction of self-orthogonal algebraic geometry codes

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Quantum codes from a new construction of self-orthogonal algebraic geometry codes

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dc.contributor.author Hernando, F. es_ES
dc.contributor.author McGuire, G. es_ES
dc.contributor.author Monserrat Delpalillo, Francisco José es_ES
dc.contributor.author Moyano-Fernández, J. J. es_ES
dc.date.accessioned 2021-11-05T13:12:17Z
dc.date.available 2021-11-05T13:12:17Z
dc.date.issued 2020-02-17 es_ES
dc.identifier.issn 1570-0755 es_ES
dc.identifier.uri http://hdl.handle.net/10251/176204
dc.description.abstract [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. es_ES
dc.description.sponsorship 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. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Quantum Information Processing es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Algebraic geometry codes es_ES
dc.subject Quantum error-correction es_ES
dc.subject Algebraic curves es_ES
dc.subject Finite fields es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Quantum codes from a new construction of self-orthogonal algebraic geometry codes es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11128-020-2616-8 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-096446-B-C22/ES/VALORACIONES, FOLIACIONES Y CODIGOS CORRECTORES DE ERRORES CUANTICOS/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/SFI//13%2FIA%2F1914/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2015-65764-C3-2-P/ES/VALORACIONES, CAMPOS VECTORIALES ALGEBRAICOS Y CODIGOS CORRECTORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2015-65764-C3-2-P//VALORACIONES, CAMPOS VECTORIALES ALGEBRAICOS Y CODIGOS CORRECTORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UJI//UJI-B2018-10/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//AICO%2F2019%2F223//CONJUNTOS CONVEXOS ASOCIADOS A SUPERFICIES Y CODIGOS CORRECTORES DE ERRORES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation 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 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s11128-020-2616-8 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 25 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 19 es_ES
dc.description.issue 4 es_ES
dc.relation.pasarela S\430288 es_ES
dc.contributor.funder Universitat Jaume I es_ES
dc.contributor.funder GENERALITAT VALENCIANA es_ES
dc.contributor.funder Science Foundation Ireland es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.contributor.funder Ministerio de Ciencia, Innovación y Universidades es_ES
dc.description.references Abhyankar, S.S.: Irreducibility criterion for germs of analytic functions of two complex variables. Adv. Math. 74, 190–257 (1989) es_ES
dc.description.references Abhyankar, S.S.: Algebraic Geometry for Scientists and Engineers. Mathematical Surveys and Monographs, American Mathematical Society, Providence (1990) es_ES
dc.description.references Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection I: statement of the problem. IEEE Trans. Inf. Theory 46, 778–788 (2000) es_ES
dc.description.references Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection II: bounds. IEEE Trans. Inf. Theory 46, 789–800 (2000) es_ES
dc.description.references Ashikhmin, A., Knill, E.: Non-binary quantum stabilizer codes. IEEE Trans. Inf. Theory 47, 3065–3072 (2001) es_ES
dc.description.references Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997) es_ES
dc.description.references Bierbrauer, J., Edel, Y.: Quantum twisted codes. J. Comb. Des. 8, 174–188 (2000) es_ES
dc.description.references 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) es_ES
dc.description.references Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996) es_ES
dc.description.references Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory 44(4), 1369–1387 (1998) es_ES
dc.description.references Campillo, A., Farrán, J.I.: Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models. Finite Fields Appl. 6, 71–92 (2000) es_ES
dc.description.references Duursma, I.M.: Algebraic geometry codes: general theory. In: Advances in Algebraic Geometry Codes, Series of Coding Theory and Cryptology, vol. 5. World Scientific, Singapore (2008) es_ES
dc.description.references Feng, K.: Quantum error correcting codes. In: Coding Theory and Cryptology, pp. 91–142. Word Scientific (2002) es_ES
dc.description.references Feng, K., Ma, Z.: A finite Gilbert–Varshamov bound for pure stabilizer quantum codes. IEEE Trans. Inf. Theory 50, 3323–3325 (2004) es_ES
dc.description.references Galindo, C., Geil, O., Hernando, F., Ruano, D.: On the distance of stabilizer quantum codes from $$J$$-affine variety codes. Quantum Inf. Process 16, 111 (2017) es_ES
dc.description.references Galindo, C., Hernando, F., Matsumoto, R.: Quasi-cyclic construction of quantum codes. Finite Fields Appl. 52, 261–280 (2018) es_ES
dc.description.references Galindo, C., Hernando, F., Ruano, D.: Stabilizer quantum codes from $$J$$-affine variety codes and a new Steane-like enlargement. Quantum Inf. Process 14, 3211–3231 (2015) es_ES
dc.description.references Galindo, C., Hernando, F., Ruano, D.: Classical and quantum evaluation codes at the trace roots. IEEE Trans. Inf. Theory 16, 2593–2602 (2019) es_ES
dc.description.references Garcia, A.: On AG codes and Artin–Schreier extensions. Commun. Algebra 20(12), 3683–3689 (1992) es_ES
dc.description.references Goppa, V.D.: Geometry and Codes. Mathematics and its Applications, vol. 24. Kluwer, Dordrecht (1991) es_ES
dc.description.references Goppa, V.D.: Codes associated with divisors. Probl. Inf. Transm. 13, 22–26 (1977) es_ES
dc.description.references Gottesman, D.: A class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A 54, 1862–1868 (1996) es_ES
dc.description.references Grassl, M., Rötteler, M.: Quantum BCH codes. In: Proceedings X International Symposium Theory Electrical Engineering, pp. 207–212. Germany (1999) es_ES
dc.description.references Grassl, M., Beth, T., Rötteler, M.: On optimal quantum codes. Int. J. Quantum Inf. 2, 757–775 (2004) es_ES
dc.description.references He, X., Xu, L., Chen, H.: New $$q$$-ary quantum MDS codes with distances bigger than $$q/2$$. Quantum Inf. Process. 15(7), 2745–2758 (2016) es_ES
dc.description.references Hirschfeld, J.W.P., Korchmáros, G., Torres, F.: Algebraic Curves Over a Finite Field. Princeton Series in Applied Mathematics, Princeton (2008) es_ES
dc.description.references Høholdt, T., van Lint, J., Pellikaan, R.: Algebraic geometry codes. Handb. Coding Theory 1, 871–961 (1998) es_ES
dc.description.references Jin, L., Xing, C.: Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes. IEEE Trans. Inf. Theory 58, 4489–5484 (2012) es_ES
dc.description.references Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52, 4892–4924 (2006) es_ES
dc.description.references La Guardia, G.G.: Construction of new families of nonbinary quantum BCH codes. Phys. Rev. A 80, 042331 (2009) es_ES
dc.description.references La Guardia, G.G.: On the construction of nonbinary quantum BCH codes. IEEE Trans. Inf. Theory 60, 1528–1535 (2014) es_ES
dc.description.references Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge (1994) es_ES
dc.description.references Matsumoto, R., Uyematsu, T.: Constructing quantum error correcting codes for $$p^m$$ state systems from classical error correcting codes. IEICE Trans. Fund. E83–A, 1878–1883 (2000) es_ES
dc.description.references McGuire, G., Yılmaz, E.S.: Divisibility of L-polynomials for a family of Artin–Schreier curves. J. Pure Appl. Algebra 223(8), 3341–3358 (2019) es_ES
dc.description.references Munuera, C., Sepúlveda, A., Torres, F.: Castle curves and codes. Adv. Math. Commun. 3, 399–408 (2009) es_ES
dc.description.references Munuera, C., Tenório, W., Torres, F.: Quantum error-correcting codes from algebraic geometry codes of castle type. Quantum Inf. Process. 15, 4071–4088 (2016) es_ES
dc.description.references Pellikaan, R., Shen, B.Z., van Wee, G.J.M.: Which linear codes are algebraic-geometric. IEEE Trans. Inf. Theory 37, 583–602 (1991) es_ES
dc.description.references Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE Computer Society Press (1994) es_ES
dc.description.references Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493 (1995) es_ES
dc.description.references Steane, A.M.: Multiple-particle interference and quantum error correction. Proc. R. Soc. Lond. Ser. A 452, 2551–2557 (1996) es_ES
dc.description.references Stichtenoth, H.: Algebraic Function Fields and Codes. Springer, Berlin (2009) es_ES
dc.description.references Tsfasman, M.A., Vlăduţ, S.G., Zink, T.: Modular curves, Shimura curves and AG codes, better than Varshamov–Gilbert bound. Math. Nachr. 109, 21–28 (1982) es_ES


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