References
Bush, K.A.: Orthogonal arrays of index unity. Ann. Math. Stat.23, 426–434 (1952)
Bruen, A.A., Silverman, R.: On the non-existence of certain M.D.S. codes and projective planes. Math. Z.183, 171–175 (1983)
Casse, L.R.A.: A solution to B. Segre's problemI r,q . VII Österreichischer Mathematikerkongress, Linz, 1968
Casse, L.R.A., Glynn, D.G.: The solution to Beniamino Segre's problemI r,q ,r=3,q=2h. Geom. Dedicata13, 157–163 (1982)
Casse, L.R.A., Glynn, D.G.: On the uniqueness of (q+1)4-arcs ofPG(4,q),q=2h,h≧3. Discrete Math.48, 173–186 (1984)
Dembowski, P.: Finite geometries. Berlin-Heidelberg-New York: Springer 1968
Glynn, D.G.: The non-classical 10-arc ofPG(4, 9). Discrete Math.59, 43–51 (1986)
Hill, R.: A first course in coding theory. Oxford: Clarendon Press 1986
Hirschfeld, J.W.P.: Projective geometries over finite fields. Oxford: Clarendon Press 1979
Hirschfeld, J.W.P.: Finite projective spaces of three dimensions. Oxford: Clarendon Press 1985
MacWilliams, F.J., Sloane, N.J.A.: The theory of error-correcting codes. Amsterdam: North-Holland 1977
Maneri, C., Silverman, R.: A combinatorial problem with applications to geometry. J. Comb. Theory, Ser. A11, 118–121 (1971)
Segre, B.: Curve razionali normali ek-archi negli spazi finite. Ann. Mat. Pura Appl., IV. Ser.39, 357–379 (1955)
Segre, B.: Lectures on modern geometry, Ed. Roma: Cremonese 1961
Segre, B.: Introduction to galois geometries. Mem. Accad. Naz. Lincei8, 133–236 (1967)
Semple, J.G., Roth, L.: Introduction to algebraic geometry. Oxford: Clarendon Press 1985
Seroussi, G., Roth, R.M.: On M.D.S. extensions of generalized Reed — Solomon codes. IEEE Trans. Infor. Theory
Singleton, R.C.: Maximum distanceq-nary codes. IEEE Trans. Inf. Theory10, 116–118 (1964)
Thas, J.A.: Normal rational curves andk-arcs in Galois spaces. Rend. Mat. (6)1, 331–334 (1968)
Thas, J.A.: Connection between the GrassmannianG k−1;n and the set of thek-arcs of the Galois spaceS n,q . Rend. Mat. (6)2, 121–134 (1969)
Thas, J.A.: Normal rational curves and (q+2)-arcs in a Galois spaceS q−2,q (q=2h). Rend. Accad. Naz. Lincei47, 249–252 (1969)
Thas, J.A.: Complete arcs and algebraic curves inPG(2,q). J. Algebra (in press)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bruen, A.A., Thas, J.A. & Blokhuis, A. On M.D.S. codes, arcs inPG(n, q) withq even, and a solution of three fundamental problems of B. Segre. Invent Math 92, 441–459 (1988). https://doi.org/10.1007/BF01393742
Issue Date:
DOI: https://doi.org/10.1007/BF01393742