{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:36:23Z","timestamp":1773232583361,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2012,8,30]],"date-time":"2012-08-30T00:00:00Z","timestamp":1346284800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2014,1]]},"DOI":"10.1007\/s10623-012-9738-7","type":"journal-article","created":{"date-parts":[[2012,8,29]],"date-time":"2012-08-29T11:56:44Z","timestamp":1346241404000},"page":"189-213","source":"Crossref","is-referenced-by-count":5,"title":["Evaluation codes defined by finite families of plane valuations at infinity"],"prefix":"10.1007","volume":"70","author":[{"given":"C.","family":"Galindo","sequence":"first","affiliation":[]},{"given":"F.","family":"Monserrat","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,8,30]]},"reference":[{"key":"9738_CR1","doi-asserted-by":"crossref","first-page":"491","DOI":"10.2307\/1970014","volume":"63","author":"S.S. Abhyankar","year":"1956","unstructured":"Abhyankar S.S.: Local uniformization on algebraic surfaces over ground field of characteristic p \u2260\u00a00. Ann. Math. 63, 491\u2013526 (1956)","journal-title":"Ann. Math."},{"key":"9738_CR2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.2307\/2372519","volume":"78","author":"S.S. Abhyankar","year":"1956","unstructured":"Abhyankar S.S.: On the valuations centered in a local domain. Am. J. Math. 78, 321\u2013348 (1956)","journal-title":"Am. J. Math."},{"key":"9738_CR3","unstructured":"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)."},{"key":"9738_CR4","unstructured":"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\u2013414 (1977)."},{"key":"9738_CR5","first-page":"47","volume":"260","author":"S.S. Abhyankar","year":"1973","unstructured":"Abhyankar S.S., Moh T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation (I). J. Reine Angew. Math. 260, 47\u201383 (1973)","journal-title":"J. Reine Angew. Math."},{"key":"9738_CR6","first-page":"29","volume":"261","author":"S.S. Abhyankar","year":"1973","unstructured":"Abhyankar S.S., Moh T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation (II). J. Reine Angew. Math. 261, 29\u201354 (1973)","journal-title":"J. Reine Angew. Math."},{"key":"9738_CR7","volume-title":"Algebraic Coding Theory","author":"E.R. Berlekamp","year":"1968","unstructured":"Berlekamp E.R.: Algebraic Coding Theory. McGraw-Hill, New York (1968)"},{"key":"9738_CR8","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1006\/ffta.1999.0266","volume":"6","author":"A. Campillo","year":"2000","unstructured":"Campillo A., Farr\u00e1n J.I.: Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models. Finite Fields Appl. 6, 71\u201392 (2000)","journal-title":"Finite Fields Appl."},{"key":"9738_CR9","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1109\/TIT.2007.894663","volume":"53","author":"C. Carvalho","year":"2007","unstructured":"Carvalho C., Munuera C., Silva E., Torres F.: Near orders and codes. IEEE Trans. Inf. Theory 53, 1919\u20131924 (2007)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR10","unstructured":"Decker W., Greuel G.M., Pfister G., Sch\u00f6enemann H.: Singular 3.1.3, a computer algebra system for polynomial computations (2011) http:\/\/www.singular.uni-kl.de ."},{"key":"9738_CR11","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/18.179340","volume":"39","author":"G.L. Feng","year":"1993","unstructured":"Feng G.L., Rao T.R.N.: Decoding of algebraic geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 39, 37\u201345 (1993)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR12","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1109\/18.335972","volume":"40","author":"G.L. Feng","year":"1994","unstructured":"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\u20131012 (1994)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR13","doi-asserted-by":"crossref","first-page":"1678","DOI":"10.1109\/18.476241","volume":"41","author":"G.L. Feng","year":"1995","unstructured":"Feng G.L., Rao T.R.N.: Improved geometric Goppa codes, part I: basic theory. IEEE Trans. Inf. Theory 41, 1678\u20131693 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"9738_CR14","first-page":"1005","volume":"39","author":"M. Fujimoto","year":"2002","unstructured":"Fujimoto M., Suzuki M.: Construction of affine plane curves with one place at infinity. Osaka J. Math. 39(4), 1005\u20131027 (2002)","journal-title":"Osaka J. Math."},{"issue":"6","key":"9738_CR15","doi-asserted-by":"crossref","first-page":"2107","DOI":"10.1080\/00927879508825332","volume":"23","author":"C. Galindo","year":"1995","unstructured":"Galindo C.: Plane valuations and their completions. Commun. Algebra 23(6), 2107\u20132123 (1995)","journal-title":"Commun. Algebra"},{"key":"9738_CR16","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1112\/plms\/pdn042","volume":"98","author":"C. Galindo","year":"2009","unstructured":"Galindo C., Monserrat F.: \u03b4-sequences and evaluation codes defined by plane valuations at infinity. Proc. Lond. Math. Soc. 98, 714\u2013740 (2009)","journal-title":"Proc. Lond. Math. Soc."},{"key":"9738_CR17","unstructured":"Galindo C., Monserrat F.: The Abhyankar-Moh theorem for plane valuations at infinity. Preprint 2010. ArXiv:0910.2613v2."},{"issue":"2","key":"9738_CR18","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s10623-006-9011-z","volume":"41","author":"C. Galindo","year":"2006","unstructured":"Galindo C., Sanchis M.: Evaluation codes and plane valuations. Des. Codes Cryptogr. 41(2), 199\u2013219 (2006)","journal-title":"Des. Codes Cryptogr."},{"key":"9738_CR19","unstructured":"Geil O.: Codes based on an $${\\mathbb{F}_q}$$ -algebra. PhD Thesis, Aalborg University, June (2000)."},{"key":"9738_CR20","doi-asserted-by":"crossref","unstructured":"Geil O., Matsumoto R.: Generalized Sudan\u2019s list decoding for order domain codes. Lecture Notes in Computer Science, vol. 4851, pp. 50\u201359 (2007)","DOI":"10.1007\/978-3-540-77224-8_9"},{"key":"9738_CR21","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1006\/ffta.2001.0347","volume":"8","author":"O. Geil","year":"2002","unstructured":"Geil O., Pellikaan R.: On the structure of order domains. Finite Fields Appl. 8, 369\u2013396 (2002)","journal-title":"Finite Fields Appl."},{"key":"9738_CR22","first-page":"22","volume":"13","author":"V.D. Goppa","year":"1997","unstructured":"Goppa V.D.: Codes associated with divisors. Probl. Inf. Transm. 13, 22\u201326 (1997)","journal-title":"Probl. Inf. Transm."},{"key":"9738_CR23","unstructured":"Goppa V.D.: Geometry and Codes. Mathematics and Its Applications, vol. 24. Kluwer, Dordrecht (1991)."},{"key":"9738_CR24","unstructured":"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\u2013455. Springer, Berlin (2003)."},{"key":"9738_CR25","unstructured":"H\u00f8holdt T., van Lint J.H., Pellikaan R.: Algebraic geometry codes. In: Handbook of Coding Theory, vol. 1, pp. 871\u2013961. Elsevier, Amsterdam (1998)."},{"key":"9738_CR26","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/18.335910","volume":"40","author":"C.D. Jensen","year":"1994","unstructured":"Jensen C.D.: Fast decoding of codes from algebraic geometry. IEEE Trans. Inf. Theory 40, 223\u2013230 (1994)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR27","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1109\/18.32157","volume":"35","author":"J. Justesen","year":"1989","unstructured":"Justesen J., Larsen K.J., Jensen H.E., Havemose A., H\u00f8holdt T.: Construction and decoding of a class of algebraic geometric codes. IEEE Trans. Inf. Theory 35, 811\u2013821 (1989)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR28","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1109\/18.108255","volume":"38","author":"J. Justesen","year":"1992","unstructured":"Justesen J., Larsen K.J., Jensen H.E., H\u00f8holdt T.: Fast decoding of codes from algebraic plane curves. IEEE Trans. Inf. Theory 38, 111\u2013119 (1992)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR29","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/TIT.1969.1054260","volume":"15","author":"J.L. Massey","year":"1969","unstructured":"Massey J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Inf. Theory 15, 122\u2013127 (1969)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"9738_CR30","first-page":"2007","volume":"E82-A","author":"R. Matsumoto","year":"1999","unstructured":"Matsumoto R.: Miura\u2019s generalization of one point AG codes is equivalent to H\u00f8holdt, van Lint and Pellikaan\u2019s generalization. IEICE Trans. Fundam. E82-A(10), 2007\u20132010 (1999)","journal-title":"IEICE Trans. Fundam."},{"key":"9738_CR31","first-page":"61","volume":"35","author":"M. Moghaddam","year":"2009","unstructured":"Moghaddam M.: Realization of a certain class of semigroups as value semigroups of valuations. Bull. Iran. Math. Soc. 35, 61\u201395 (2009)","journal-title":"Bull. Iran. Math. Soc."},{"key":"9738_CR32","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1109\/18.476244","volume":"41","author":"M.E. O\u2019Sullivan","year":"1995","unstructured":"O\u2019Sullivan M.E.: Decoding of codes defined by a single point on a curve. IEEE Trans. Inf. Theory 41, 1709\u20131719 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR33","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1006\/ffta.2000.0283","volume":"7","author":"M.E. O\u2019Sullivan","year":"2001","unstructured":"O\u2019Sullivan M.E.: New codes for the Belekamp-Massey-Sakata algorithm. Finite Fields Appl. 7, 293\u2013317 (2001)","journal-title":"Finite Fields Appl."},{"key":"9738_CR34","unstructured":"Pinkham H.: S\u00e9minaire sur les singularit\u00e9s des surfaces (Demazure-Pinkham-Teissier), Course donn\u00e9 au Centre de Math. de l\u2019Ecole Polytechnique (1977\u20131978)."},{"key":"9738_CR35","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0890-5401(90)90039-K","volume":"84","author":"S. Sakata","year":"1990","unstructured":"Sakata S.: Extension of the Berlekamp-Massey algorithm to N dimensions. Inf. Comput. 84, 207\u2013239 (1990)","journal-title":"Inf. Comput."},{"key":"9738_CR36","doi-asserted-by":"crossref","first-page":"1762","DOI":"10.1109\/18.476248","volume":"41","author":"S. Sakata","year":"1995","unstructured":"Sakata S., Jensen H.E., H\u00f8holdt T.: Generalized Berlekamp-Massey decoding of algebraic geometric codes up to half the Feng-Rao bound. IEEE Trans. Inf. Theory 41, 1762\u20131768 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR37","doi-asserted-by":"crossref","first-page":"1672","DOI":"10.1109\/18.476240","volume":"41","author":"S. Sakata","year":"1995","unstructured":"Sakata S., Justesen J., Madelung Y., Jensen H.E., H\u00f8holdt T.: Fast decoding of algebraic geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 41, 1672\u20131677 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"9738_CR38","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.2307\/2374003","volume":"99","author":"A. Sathaye","year":"1977","unstructured":"Sathaye A.: On planar curves. Am. J. Math. 99(5), 1105\u20131135 (1977)","journal-title":"Am. J. Math."},{"key":"9738_CR39","doi-asserted-by":"crossref","unstructured":"Shannon C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379\u2013423 and 623\u2013656 (1948).","DOI":"10.1002\/j.1538-7305.1948.tb00917.x"},{"key":"9738_CR40","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1109\/18.57204","volume":"36","author":"A.N. Skorobogatov","year":"1990","unstructured":"Skorobogatov A.N., Vl\u0103dut S.G.: On the decoding of algebraic geometric codes. IEEE Trans. Inf. Theory 36, 1051\u20131060 (1990)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9738_CR41","doi-asserted-by":"crossref","first-page":"107","DOI":"10.2307\/2374856","volume":"112","author":"M. Spivakovsky","year":"1990","unstructured":"Spivakovsky M.: Valuations in function fields of surfaces. Am. J. Math. 112, 107\u2013156 (1990)","journal-title":"Am. J. Math."},{"issue":"2","key":"9738_CR42","doi-asserted-by":"crossref","first-page":"375","DOI":"10.5802\/aif.1678","volume":"49","author":"M. Suzuki","year":"1999","unstructured":"Suzuki M.: Affine plane curves with one place at infinity. Ann. Inst. Fourier 49(2), 375\u2013404 (1999)","journal-title":"Ann. Inst. Fourier"},{"key":"9738_CR43","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1002\/mana.19821090103","volume":"109","author":"S.G. Tsfasman","year":"1982","unstructured":"Tsfasman S.G., Vl\u0103du\u0163 T.: Zink, modular curves, Shimura curves and Goppa codes, better than Varshamov\u2013Gilbert bound. Math. Nachr. 109, 21\u201328 (1982)","journal-title":"Math. Nachr."},{"key":"9738_CR44","unstructured":"Vl\u0103du\u0163 S.G., Manin Y.I. Linear codes and modular curves. In: Current problems in mathematics, vol. 25, pp. 209\u2013257. Akad. Nauk SSSR Vseoyuz, Moscow (1984)."},{"key":"9738_CR45","doi-asserted-by":"crossref","first-page":"639","DOI":"10.2307\/1968949","volume":"40","author":"O. Zariski","year":"1939","unstructured":"Zariski O.: The reduction of the singularities of an algebraic surface. Ann. Math. 40, 639\u2013689 (1939)","journal-title":"Ann. Math."},{"key":"9738_CR46","doi-asserted-by":"crossref","first-page":"852","DOI":"10.2307\/1968864","volume":"41","author":"O. Zariski","year":"1940","unstructured":"Zariski O.: Local uniformization on algebraic varieties. Ann. Math. 41, 852\u2013896 (1940)","journal-title":"Ann. Math."},{"key":"9738_CR47","doi-asserted-by":"crossref","unstructured":"Zariski O., Samuel P.(1960) Commutative Algebra, vol. II. Springer, Berlin.","DOI":"10.1007\/978-3-662-29244-0"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-012-9738-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-012-9738-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-012-9738-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,3]],"date-time":"2019-07-03T05:46:20Z","timestamp":1562132780000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-012-9738-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,30]]},"references-count":47,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["9738"],"URL":"https:\/\/doi.org\/10.1007\/s10623-012-9738-7","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,30]]}}}