Nuclei of sets of q+1 points in PG(2,q) and blocking sets of Redei type
Journal of Combinatorial Theory Series A
Error control systems for digital communication and storage
Error control systems for digital communication and storage
On the number of slopes of the graph of a function defined on a finite field
Journal of Combinatorial Theory Series A
The number of directions determined by a function over a finite field
Journal of Combinatorial Theory Series A
Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century
Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century
On the maximality of linear codes
Designs, Codes and Cryptography
Cubic Curves, Finite Geometry and Cryptography
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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Given any linear code C over a finite field GF(q) we show how C can be described in a transparent and geometrical way by using the associated Bruen-Silverman code. Then, specializing to the case of MDS codes we use our new approach to offer improvements to the main results currently available concerning MDS extensions of linear MDS codes. We also sharply limit the possibilities for constructing long non-linear MDS codes. Our proofs make use of the connection between the work of Redei [L. Redei, Lacunary Polynomials over Finite Fields, North-Holland, Amsterdam, 1973. Translated from the German by I. Foldes. [18]] and the Redei blocking sets that was first pointed out over thirty years ago in [A.A. Bruen, B. Levinger, A theorem on permutations of a finite field, Canad. J. Math. 25 (1973) 1060-1065]. The main results of this paper significantly strengthen those in [A. Blokhuis, A.A. Bruen, J.A. Thas, Arcs in PG(n,q), MDS-codes and three fundamental problems of B. Segre-Some extensions, Geom. Dedicata 35 (1-3) (1990) 1-11; A.A. Bruen, J.A. Thas, A.Blokhuis, On M.D.S. codes, arcs in PG(n,q) with q even, and a solution of three fundamental problems of B. Segre, Invent. Math. 92 (3) (1988) 441-459].