Maximum distance separable codes and arcs in projective spaces
Copyright policy )Maximum distance separable codes and arcs in projective spaces
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.
18 Pages; co-author added; some results updated; references added
- University of New Brunswick Canada
- University of Calgary Canada
- Wright State University United States
- University System of Ohio United States
Combinatorial structures in finite projective spaces, code extensions, dual arcs, Finite partial geometries (general), nets, partial spreads, linear codes, Theoretical Computer Science, Linear codes, arcs, Code extensions, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorial codes, Blocking sets, ovals, \(k\)-arcs, 51E21, 94B27, Computational Theory and Mathematics, Combinatorial aspects of finite geometries, MDS codes, Combinatorics (math.CO), Arcs, Complete arcs, complete arcs, Dual arcs
Combinatorial structures in finite projective spaces, code extensions, dual arcs, Finite partial geometries (general), nets, partial spreads, linear codes, Theoretical Computer Science, Linear codes, arcs, Code extensions, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorial codes, Blocking sets, ovals, \(k\)-arcs, 51E21, 94B27, Computational Theory and Mathematics, Combinatorial aspects of finite geometries, MDS codes, Combinatorics (math.CO), Arcs, Complete arcs, complete arcs, Dual arcs
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