{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:02:53Z","timestamp":1772283773924,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540606932","type":"print"},{"value":"9783540492801","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1995]]},"DOI":"10.1007\/3-540-60693-9_7","type":"book-chapter","created":{"date-parts":[[2012,2,26]],"date-time":"2012-02-26T20:54:29Z","timestamp":1330289669000},"page":"44-52","source":"Crossref","is-referenced-by-count":10,"title":["The main conjecture for MDS codes"],"prefix":"10.1007","author":[{"given":"J. W. P.","family":"Hirschfeld","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,6,7]]},"reference":[{"key":"7_CR1","unstructured":"A.H. Ali, Classification of arcs in the plane of order 13, Ph.D. thesis, University of Sussex, 1993."},{"key":"7_CR2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1002\/jcd.3180020304","volume":"2","author":"A.H. Ali","year":"1994","unstructured":"A.H. Ali, J.W.P. Hirschfeld and H. Kaneta, The automorphism group of a complete (q\u22121)-arc in PG(2, q), J. Combin. Designs 2 (1994), 131\u2013145.","journal-title":"J. Combin. Designs"},{"key":"7_CR3","doi-asserted-by":"crossref","unstructured":"A.H. Ali, J.W.P. Hirschfeld and H. Kaneta, On the size of arcs in projective spaces, IEEE Trans. Inform. Theory, to appear.","DOI":"10.1109\/18.476237"},{"key":"7_CR4","unstructured":"J.M. Chao and H. Kaneta, Rational arcs in PG(r, q) for 11\u2264 q\u226419, preprint."},{"key":"7_CR5","unstructured":"J.M. Chao and H. Kaneta, Rational arcs in PG(r, q) for 23\u2264 q\u226427, preprint."},{"key":"7_CR6","first-page":"243","volume-title":"Combinatorics '84, Ann. Discrete Math. 30, North-Holland Mathematics Studies 123","author":"J.C. Fisher","year":"1986","unstructured":"J.C. Fisher. J.W.P. Hirschfeld and J.A. Thas, Complete arcs in planes of square order, Combinatorics '84, Ann. Discrete Math. 30, North-Holland Mathematics Studies 123, North-Holland, Amsterdam, 1986, 243\u2013250."},{"key":"7_CR7","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0012-365X(86)90067-1","volume":"59","author":"D.G. Glynn","year":"1986","unstructured":"D.G. Glynn, The non-classical 10-arcs of PG(4, 9), Discrete Math. 59 (1986), 43\u201351.","journal-title":"Discrete Math."},{"key":"7_CR8","series-title":"London Math. Soc. Lecture Notes 191","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1017\/CBO9780511526336.017","volume-title":"Finite Geometry and Combinatorics","author":"C.E. Gordon","year":"1993","unstructured":"C.E. Gordon, Orbits of arcs in projective spaces, Finite Geometry and Combinatorics, London Math. Soc. Lecture Notes 191, Cambridge University Press, Cambridge, 1993, pp. 161\u2013171."},{"key":"7_CR9","volume-title":"Projective Geometries over Finite Fields","author":"J.W.P. Hirschfeld","year":"1979","unstructured":"J.W.P. Hirschfeld, Projective Geometries over Finite Fields, Oxford University Press, Oxford, 1979."},{"key":"7_CR10","series-title":"London Math. Soc. Lecture Note Series 82","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1017\/CBO9781107325548.004","volume-title":"Surveys in Combinatorics","author":"J.W.P. Hirschfeld","year":"1983","unstructured":"J.W.P. Hirschfeld, Maximum sets in finite projective spaces, Surveys in Combinatorics, London Math. Soc. Lecture Note Series 82, Cambridge University Press, Cambridge, 1983, pp. 55\u201376."},{"key":"7_CR11","volume-title":"Finite Projective Spaces of Three Dimensions","author":"J.W.P. Hirschfeld","year":"1985","unstructured":"J.W.P. Hirschfeld, Finite Projective Spaces of Three Dimensions, Oxford University Press, Oxford, 1985."},{"key":"7_CR12","unstructured":"J.W.P. Hirschfeld, Complete arcs, Combinatorics '94, to appear."},{"key":"7_CR13","doi-asserted-by":"crossref","unstructured":"J.W.P. Hirschfeld and G. Korchm\u00e1ros, On the embedding of an arc into a conic in a finite plane, Finite Fields Appl., to appear.","DOI":"10.1006\/ffta.1996.0017"},{"key":"7_CR14","doi-asserted-by":"crossref","unstructured":"J.W.P. Hirschfeld and L. Storme, The packing problem in statistics, coding theory and finite projective spaces, J. Statist. Plann. Inference, submitted.","DOI":"10.1016\/S0378-3758(98)00043-3"},{"key":"7_CR15","volume-title":"General Galois Geometries","author":"J.W.P. Hirschfeld","year":"1991","unstructured":"J.W.P. Hirschfeld and J.A. Thas, General Galois Geometries, Oxford University Press, Oxford, 1991."},{"key":"7_CR16","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1017\/S0305004100077823","volume":"105","author":"H. Kaneta","year":"1989","unstructured":"H. Kaneta and T. Maruta, An elementary proof and an extension of Thas' theorem on k-arcs, Math. Proc. Cambridge. Philos. Soc. 105 (1989), 459\u2013462.","journal-title":"Math. Proc. Cambridge. Philos. Soc."},{"key":"7_CR17","volume-title":"The Theory of Error-Correcting Codes","author":"F.J. MacWilliams","year":"1977","unstructured":"F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977."},{"key":"7_CR18","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1017\/S0305004100070146","volume":"110","author":"T. Maruta","year":"1991","unstructured":"T. Maruta and H. Kaneta, On the uniqueness of (q+1)-arcs of PG(5, q), q=2h, h\u22654, Math. Proc. Cambridge Philos. Soc. 110 (1991), 91\u201394.","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"7_CR19","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF02410779","volume":"39","author":"B. Segre","year":"1955","unstructured":"B. Segre, Curve razionali normali e k-archi negli spazi finiti, Ann. Mat. Pura Appl. 39 (1955), 357\u2013379.","journal-title":"Ann. Mat. Pura Appl."},{"key":"7_CR20","unstructured":"A.R. Sadeh, The classification of k-arcs and cubic surfaces with twenty-seven lines over the field of eleven elments, Ph.D. thesis, University of Sussex, 1984."},{"key":"7_CR21","volume-title":"Tesi di laurea","author":"M. Scipioni","year":"1990","unstructured":"M. Scipioni, Sugli archi completi nei piani desarguesiani, Tesi di laurea, University of Rome \u201cLa Sapienza\u201d, 1990."},{"key":"7_CR22","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1023\/A:1022428405084","volume":"1","author":"L. Storme","year":"1992","unstructured":"L. Storme, Completeness of normal rational curves, J. Algebraic Combin. 1 (1992), 197\u2013202.","journal-title":"J. Algebraic Combin."},{"key":"7_CR23","doi-asserted-by":"crossref","unstructured":"L. Storme and J.A. Thas, Generalized Reed-Solomon codes and normal rational curves: an improvement of results by Seroussi and Roth, Advances in Finite Geometries and Designs, Oxford University Press, 1991, 369\u2013389.","DOI":"10.1093\/oso\/9780198535928.003.0031"},{"key":"7_CR24","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/0012-365X(92)90576-2","volume":"106\/107","author":"L. Storme","year":"1992","unstructured":"L. Storme and J.A. Thas, Complete k-arcs in PG(n, q), q even, Discrete Math. 106\/107 (1992), 455\u2013469.","journal-title":"Discrete Math."},{"key":"7_CR25","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/0097-3165(93)90076-K","volume":"62","author":"L. Storme","year":"1993","unstructured":"L. Storme and J.A. Thas, M.D.S. codes and arcs in PG(n, q) with q even: an improvement of the bounds of Bruen, Thas, and Blokhuis, J. Combin. Theory Ser. A 62 (1993), 139\u2013154.","journal-title":"J. Combin. Theory Ser. A"},{"key":"7_CR26","first-page":"121","volume":"2","author":"J.A. Thas","year":"1969","unstructured":"J.A. Thas, Connection between the Grassmannian Gk\u22121;n and the set of k-arcs of the Galois space S n,q , Rend. Mat. 2 (1969), 121\u2013134.","journal-title":"Rend. Mat."},{"key":"7_CR27","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/0021-8693(87)90007-X","volume":"106","author":"J.A. Thas","year":"1987","unstructured":"J.A. Thas, Complete arcs and algebraic curves in PG(2, q), J. Algebra 106 (1987), 451\u2013464.","journal-title":"J. Algebra"},{"key":"7_CR28","first-page":"315","volume":"47","author":"J.A. Thas","year":"1992","unstructured":"J.A. Thas, M.D.S. codes and arcs in projective spaces, Le Matematiche 47 (1992), 315\u2013328.","journal-title":"Le Matematiche"},{"key":"7_CR29","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1007\/BF01222904","volume":"38","author":"J.F. Voloch","year":"1990","unstructured":"J.F. Voloch, Arcs in projective planes over prime fields, J. Geom. 38 (1990), 198\u2013200.","journal-title":"J. Geom."},{"key":"7_CR30","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1093\/oso\/9780198535928.003.0033","volume-title":"Advances in Finite Geometries and Designs","author":"J.F. Voloch","year":"1991","unstructured":"J.F. Voloch, Complete arcs in Galois planes of non-square order, Advances in Finite Geometries and Designs, Oxford University Press, Oxford, 1991, pp. 401\u2013406."}],"container-title":["Lecture Notes in Computer Science","Cryptography and Coding"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-60693-9_7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,20]],"date-time":"2024-04-20T17:06:18Z","timestamp":1713632778000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-60693-9_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995]]},"ISBN":["9783540606932","9783540492801"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/3-540-60693-9_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995]]}}}