- -

Evaluation codes defined by finite families of plane valuations at infinity

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Evaluation codes defined by finite families of plane valuations at infinity

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Evaluation codes ...
Tamaño: 353.0Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: Evaluation codes.pdf
Tamaño: 343.5Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Galindo Pastor, Carlos es_ES
dc.contributor.author Monserrat Delpalillo, Francisco José es_ES
dc.date.accessioned 2015-05-20T10:39:15Z
dc.date.available 2015-05-20T10:39:15Z
dc.date.issued 2014-01
dc.identifier.issn 0925-1022
dc.identifier.uri http://hdl.handle.net/10251/50544
dc.description.abstract We construct evaluation codes given by weight functions defined over polynomial rings in m a parts per thousand yen 2 indeterminates. These weight functions are determined by sets of m-1 weight functions over polynomial rings in two indeterminates defined by plane valuations at infinity. Well-suited families in totally ordered commutative groups are an important tool in our procedure es_ES
dc.description.sponsorship Supported by Spain Ministry of Education MTM2007-64704 and Bancaixa P1-1B2009-03. The authors thank to the referees for their valuable suggestions. en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Designs, Codes and Cryptography es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Error-correcting codes es_ES
dc.subject Algebraic Geometric Codes es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Evaluation codes defined by finite families of plane valuations at infinity es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10623-012-9738-7
dc.relation.projectID info:eu-repo/grantAgreement/MEC//MTM2007-64704/ES/GEOMETRIA ALGEBRAICA DE LAS SINGULARIDADES, COMPUTACION E INFORMACION/
dc.relation.projectID info:eu-repo/grantAgreement/Fundación Bancaja//P1-132009-03/
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 Galindo Pastor, C.; Monserrat Delpalillo, FJ. (2014). Evaluation codes defined by finite families of plane valuations at infinity. Designs, Codes and Cryptography. 70(1-2):189-213. https://doi.org/10.1007/s10623-012-9738-7 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s10623-012-9738-7 es_ES
dc.description.upvformatpinicio 189 es_ES
dc.description.upvformatpfin 213 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 70 es_ES
dc.description.issue 1-2 es_ES
dc.relation.senia 278482
dc.contributor.funder Fundación Bancaja es_ES
dc.contributor.funder Ministerio de Educación y Ciencia es_ES
dc.description.references Abhyankar S.S.: Local uniformization on algebraic surfaces over ground field of characteristic p ≠ 0. Ann. Math. 63, 491–526 (1956) es_ES
dc.description.references Abhyankar S.S.: On the valuations centered in a local domain. Am. J. Math. 78, 321–348 (1956) es_ES
dc.description.references Abhyankar S.S.: Lectures on expansion techniques in algebraic geometry. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 57. Tata Institute of Fundamental Research, Bombay (1977). es_ES
dc.description.references Abhyankar S.S.: On the semigroup of a meromorphic curve (part I). In: Proceedings of the International Symposium on Algebraic Geometry (Kyoto) Kinokunio Tokio, pp. 249–414 (1977). es_ES
dc.description.references Abhyankar S.S., Moh T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation (I). J. Reine Angew. Math. 260, 47–83 (1973) es_ES
dc.description.references Abhyankar S.S., Moh T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation (II). J. Reine Angew. Math. 261, 29–54 (1973) es_ES
dc.description.references Berlekamp E.R.: Algebraic Coding Theory. McGraw-Hill, New York (1968) 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 Carvalho C., Munuera C., Silva E., Torres F.: Near orders and codes. IEEE Trans. Inf. Theory 53, 1919–1924 (2007) es_ES
dc.description.references Decker W., Greuel G.M., Pfister G., Schöenemann H.: Singular 3.1.3, a computer algebra system for polynomial computations (2011) http://www.singular.uni-kl.de . es_ES
dc.description.references Feng G.L., Rao T.R.N.: Decoding of algebraic geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 39, 37–45 (1993) es_ES
dc.description.references Feng G.L., Rao T.R.N.: A simple approach for construction of algebraic-geometric codes from affine plane curves. IEEE Trans. Inf. Theory 40, 1003–1012 (1994) es_ES
dc.description.references Feng G.L., Rao T.R.N.: Improved geometric Goppa codes, part I: basic theory. IEEE Trans. Inf. Theory 41, 1678–1693 (1995) es_ES
dc.description.references Fujimoto M., Suzuki M.: Construction of affine plane curves with one place at infinity. Osaka J. Math. 39(4), 1005–1027 (2002) es_ES
dc.description.references Galindo C.: Plane valuations and their completions. Commun. Algebra 23(6), 2107–2123 (1995) es_ES
dc.description.references Galindo C., Monserrat F.: δ-sequences and evaluation codes defined by plane valuations at infinity. Proc. Lond. Math. Soc. 98, 714–740 (2009) es_ES
dc.description.references Galindo C., Monserrat F.: The Abhyankar-Moh theorem for plane valuations at infinity. Preprint 2010. ArXiv:0910.2613v2. es_ES
dc.description.references Galindo C., Sanchis M.: Evaluation codes and plane valuations. Des. Codes Cryptogr. 41(2), 199–219 (2006) es_ES
dc.description.references Geil O.: Codes based on an $${\mathbb{F}_q}$$ -algebra. PhD Thesis, Aalborg University, June (2000). es_ES
dc.description.references Geil O., Matsumoto R.: Generalized Sudan’s list decoding for order domain codes. Lecture Notes in Computer Science, vol. 4851, pp. 50–59 (2007) es_ES
dc.description.references Geil O., Pellikaan R.: On the structure of order domains. Finite Fields Appl. 8, 369–396 (2002) es_ES
dc.description.references Goppa V.D.: Codes associated with divisors. Probl. Inf. Transm. 13, 22–26 (1997) 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 Greco S., Kiyek K.: General elements in complete ideals and valuations centered at a two-dimensional regular local ring. In: Algebra, Arithmetic, and Geometry, with Applications, pp. 381–455. Springer, Berlin (2003). es_ES
dc.description.references Høholdt T., van Lint J.H., Pellikaan R.: Algebraic geometry codes. In: Handbook of Coding Theory, vol. 1, pp. 871–961. Elsevier, Amsterdam (1998). es_ES
dc.description.references Jensen C.D.: Fast decoding of codes from algebraic geometry. IEEE Trans. Inf. Theory 40, 223–230 (1994) es_ES
dc.description.references Justesen J., Larsen K.J., Jensen H.E., Havemose A., Høholdt T.: Construction and decoding of a class of algebraic geometric codes. IEEE Trans. Inf. Theory 35, 811–821 (1989) es_ES
dc.description.references Justesen J., Larsen K.J., Jensen H.E., Høholdt T.: Fast decoding of codes from algebraic plane curves. IEEE Trans. Inf. Theory 38, 111–119 (1992) es_ES
dc.description.references Massey J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Inf. Theory 15, 122–127 (1969) es_ES
dc.description.references Matsumoto R.: Miura’s generalization of one point AG codes is equivalent to Høholdt, van Lint and Pellikaan’s generalization. IEICE Trans. Fundam. E82-A(10), 2007–2010 (1999) es_ES
dc.description.references Moghaddam M.: Realization of a certain class of semigroups as value semigroups of valuations. Bull. Iran. Math. Soc. 35, 61–95 (2009) es_ES
dc.description.references O’Sullivan M.E.: Decoding of codes defined by a single point on a curve. IEEE Trans. Inf. Theory 41, 1709–1719 (1995) es_ES
dc.description.references O’Sullivan M.E.: New codes for the Belekamp-Massey-Sakata algorithm. Finite Fields Appl. 7, 293–317 (2001) es_ES
dc.description.references Pinkham H.: Séminaire sur les singularités des surfaces (Demazure-Pinkham-Teissier), Course donné au Centre de Math. de l’Ecole Polytechnique (1977–1978). es_ES
dc.description.references Sakata S.: Extension of the Berlekamp-Massey algorithm to N dimensions. Inf. Comput. 84, 207–239 (1990) es_ES
dc.description.references Sakata S., Jensen H.E., Høholdt T.: Generalized Berlekamp-Massey decoding of algebraic geometric codes up to half the Feng-Rao bound. IEEE Trans. Inf. Theory 41, 1762–1768 (1995) es_ES
dc.description.references Sakata S., Justesen J., Madelung Y., Jensen H.E., Høholdt T.: Fast decoding of algebraic geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 41, 1672–1677 (1995) es_ES
dc.description.references Sathaye A.: On planar curves. Am. J. Math. 99(5), 1105–1135 (1977) es_ES
dc.description.references Shannon C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 and 623–656 (1948). es_ES
dc.description.references Skorobogatov A.N., Vlădut S.G.: On the decoding of algebraic geometric codes. IEEE Trans. Inf. Theory 36, 1051–1060 (1990) es_ES
dc.description.references Spivakovsky M.: Valuations in function fields of surfaces. Am. J. Math. 112, 107–156 (1990) es_ES
dc.description.references Suzuki M.: Affine plane curves with one place at infinity. Ann. Inst. Fourier 49(2), 375–404 (1999) es_ES
dc.description.references Tsfasman S.G., Vlăduţ T.: Zink, modular curves, Shimura curves and Goppa codes, better than Varshamov–Gilbert bound. Math. Nachr. 109, 21–28 (1982) es_ES
dc.description.references Vlăduţ S.G., Manin Y.I. Linear codes and modular curves. In: Current problems in mathematics, vol. 25, pp. 209–257. Akad. Nauk SSSR Vseoyuz, Moscow (1984). es_ES
dc.description.references Zariski O.: The reduction of the singularities of an algebraic surface. Ann. Math. 40, 639–689 (1939) es_ES
dc.description.references Zariski O.: Local uniformization on algebraic varieties. Ann. Math. 41, 852–896 (1940) es_ES
dc.description.references Zariski O., Samuel P.(1960) Commutative Algebra, vol. II. Springer, Berlin. es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem