{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T11:41:08Z","timestamp":1725536468756},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642036842"},{"type":"electronic","value":"9783642036859"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-03685-9_40","type":"book-chapter","created":{"date-parts":[[2009,8,21]],"date-time":"2009-08-21T02:39:51Z","timestamp":1250822391000},"page":"534-547","source":"Crossref","is-referenced-by-count":14,"title":["Succinct Representation of Codes with Applications to Testing"],"prefix":"10.1007","author":[{"given":"Elena","family":"Grigorescu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tali","family":"Kaufman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Madhu","family":"Sudan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"11","key":"40_CR1","doi-asserted-by":"publisher","first-page":"4032","DOI":"10.1109\/TIT.2005.856958","volume":"51","author":"N. Alon","year":"2005","unstructured":"Alon, N., Kaufman, T., Krivelevich, M., Litsyn, S., Ron, D.: Testing Reed-Muller codes. IEEE Transactions on Information Theory\u00a051(11), 4032\u20134039 (2005)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"40_CR2","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1016\/0022-0000(93)90044-W","volume":"47","author":"M. Blum","year":"1993","unstructured":"Blum, M., Luby, M., Rubinfeld, R.: Self-testing\/correcting with applications to numerical problems. Journal of Computer and System Sciences\u00a047(3), 549\u2013595 (1993)","journal-title":"Journal of Computer and System Sciences"},{"issue":"2","key":"40_CR3","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1090\/S0894-0347-05-00476-5","volume":"18","author":"J. Bourgain","year":"2005","unstructured":"Bourgain, J.: Mordell\u2019s exponential sum estimate revisited. J. Amer. Math. Soc.\u00a018(2), 477\u2013499 (2005) (electronic)","journal-title":"J. Amer. Math. Soc."},{"key":"40_CR4","series-title":"Lecture Notes in Math.","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/978-3-540-72053-9_6","volume-title":"Geometric aspects of functional analysis","author":"J. Bourgain","year":"2007","unstructured":"Bourgain, J.: Some arithmetical applications of the sum-product theorems in finite fields. In: Geometric aspects of functional analysis. Lecture Notes in Math., vol.\u00a01910, pp. 99\u2013116. Springer, Berlin (2007)"},{"issue":"1","key":"40_CR5","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s00039-004-0451-1","volume":"14","author":"J. Bourgain","year":"2004","unstructured":"Bourgain, J., Katz, N., Tao, T.: A sum-product estimate in finite fields, and applications. Geom. Funct. Anal.\u00a014(1), 27\u201357 (2004)","journal-title":"Geom. Funct. Anal."},{"issue":"9","key":"40_CR6","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.crma.2006.01.022","volume":"342","author":"J. Bourgain","year":"2006","unstructured":"Bourgain, J., Chang, M.-C.: A Gauss sum estimate in arbitrary finite fields. C. R. Math. Acad. Sci. Paris\u00a0342(9), 643\u2013646 (2006)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"2","key":"40_CR7","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S1631-073X(03)00281-4","volume":"337","author":"J. Bourgain","year":"2003","unstructured":"Bourgain, J., Konyagin, S.V.: Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order. C. R. Math. Acad. Sci. Paris\u00a0337(2), 75\u201380 (2003)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"4","key":"40_CR8","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1145\/285055.285060","volume":"45","author":"O. Goldreich","year":"1998","unstructured":"Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. JACM\u00a045(4), 653\u2013750 (1998)","journal-title":"JACM"},{"issue":"4","key":"40_CR9","doi-asserted-by":"publisher","first-page":"558","DOI":"10.1145\/1162349.1162351","volume":"53","author":"O. Goldreich","year":"2002","unstructured":"Goldreich, O., Sudan, M.: Locally testable codes and PCPs of almost-linear length. J. ACM\u00a053(4), 558\u2013655 (2002); Preliminary version in FOCS 2002","journal-title":"J. ACM"},{"key":"40_CR10","first-page":"423","volume-title":"FOCS 2004","author":"C.S. Jutla","year":"2004","unstructured":"Jutla, C.S., Patthak, A.C., Rudra, A., Zuckerman, D.: Testing low-degree polynomials over prime fields. In: FOCS 2004, pp. 423\u2013432. IEEE Computer Society Press, Los Alamitos (2004)"},{"key":"40_CR11","first-page":"317","volume-title":"FOCS","author":"T. Kaufman","year":"2005","unstructured":"Kaufman, T., Litsyn, S.: Almost orthogonal linear codes are locally testable. In: FOCS, pp. 317\u2013326. IEEE Computer Society Press, Los Alamitos (2005)"},{"key":"40_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/11617983_28","volume-title":"Applied Algebra, Algebraic Algorithms and Error-Correcting Codes","author":"T. Kaufman","year":"2006","unstructured":"Kaufman, T., Litsyn, S.: Long extended BCH codes are spanned by minimum weight words. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds.) AAECC 2006. LNCS, vol.\u00a03857, pp. 285\u2013294. Springer, Heidelberg (2006)"},{"issue":"3","key":"40_CR13","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1137\/S0097539704445615","volume":"36","author":"T. Kaufman","year":"2006","unstructured":"Kaufman, T., Ron, D.: Testing polynomials over general fields. SIAM J. Comput.\u00a036(3), 779\u2013802 (2006)","journal-title":"SIAM J. Comput."},{"key":"40_CR14","first-page":"590","volume-title":"FOCS","author":"T. Kaufman","year":"2007","unstructured":"Kaufman, T., Sudan, M.: Sparse random linear codes are locally decodable and testable. In: FOCS, pp. 590\u2013600. IEEE Computer Society Press, Los Alamitos (2007)"},{"key":"40_CR15","first-page":"403","volume-title":"STOC","author":"T. Kaufman","year":"2008","unstructured":"Kaufman, T., Sudan, M.: Algebraic property testing: the role of invariance. In: Ladner, R.E., Dwork, C. (eds.) STOC, pp. 403\u2013412. ACM Press, New York (2008)"},{"key":"40_CR16","volume-title":"The Theory of Error-Correcting Codes","author":"F.J. MacWilliams","year":"1981","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. Elsevier\/North-Holland, Amsterdam (1981)"},{"issue":"2","key":"40_CR17","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1137\/S0097539793255151","volume":"25","author":"R. Rubinfeld","year":"1996","unstructured":"Rubinfeld, R., Sudan, M.: Robust characterizations of polynomials with applications to program testing. SIAM Journal on Computing\u00a025(2), 252\u2013271 (1996)","journal-title":"SIAM Journal on Computing"},{"key":"40_CR18","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58575-3","volume-title":"Introduction to Coding Theory","author":"J.H. Lint van","year":"1999","unstructured":"van Lint, J.H.: Introduction to Coding Theory, 3rd edn. Graduate Texts in Mathematics, vol.\u00a086. Springer, Berlin (1999)","edition":"3"}],"container-title":["Lecture Notes in Computer Science","Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-03685-9_40","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,9]],"date-time":"2019-03-09T13:49:45Z","timestamp":1552139385000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-03685-9_40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642036842","9783642036859"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-03685-9_40","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}